STHM3313 FINANCIAL ISSUES IN TOURISM & HOSPITALITY PROJECT INTRODUCTION You are currently developing a hotel project, Beautiful & Crazy (B&C) Hotel. You plan to open the hotel on January 1st, 2018 and your plan is to operate the hotel for 10 years and sell it. Now, you would like to know how the hotel will perform in the next 10 years (from 2018 – 2027) and see if the hotel would be able to attract buyers after 10 years. To predict your hotel performance, you are asked to set up income statement of the hotel for 10 years. REQUIREMENTS FOR PROJECT 1. 2. 3. You must use Microsoft Excel. Handwritten submission will not be accepted. All dollar figures should be rounded to the nearest dollar. Your submission in BLACKBOARD will be ONE file; an Excel spreadsheet. REQUIRED ANALYSIS 1. 2. 3. Prepare the income statement for 10 years (from 2018 to 2027) (Tab 1 in Excel). The format of the income statement will be discussed in the classroom. Construct the loan amortization table for 20 years (Tab 2 in Excel) to project interests expense for the 10 years. Conduct ratio analysis focusing on profit margin (%) of this hotel over the next 10 years and analyze how the profitability of the hotel is projected.  Use two decimals for the profit margin (%). 1 HOTEL B&C PROJECT GENERAL DESCRIPTION 1. 2. Hotel B&C will have “100 + Last Two Digits of Your Student ID Number” rooms. For example, if your student ID is 912345679, the hotel room number will be 179 (= 100 + 79). The project is expected to cost “$10,000,000 + (The Second Digit from the Last of Your Student ID Number × $1,000,000) in total. For example, if your student ID is 912345679, the expected cost will be $17,000,000 (= $10,000,000 + ($1,000,000 × 7)). OPERATING FORECAST 1. 2. 3. 4. 5. 6. Hotel B&C will be open 365 days per year. Hotel B&C will have three revenue generating departments: rooms, food and beverage, and other operated department. For year 1, Hotel B&C will have the overall occupancy rate of 70% in year 1, 75% in year2, and 80% thereafter. The overall ADR is expected to be “$100 + (Last Digit of Your Student ID Number × 10) in year 1 and increase at a compound annual rate of 5%. For example, if your student ID is 912345679, the overall ADR in year 1 will be $190 (= $100 + $90). The ADRs in years 2 will be $200 (=$190 × 1.05); the ADR in year 3 will be $209 (= $200 × 1.05 = $209.47, therefore, round this to the nearest dollar); the ADR in year 4 will be $220 (= $209.47 × 1.05 = $219.94, therefore, round this to the nearest dollar), and so on. Food and beverage revenue is expected to be 25% of rooms revenue in each year of the forecast. Other operated department revenue is expected to be 5% of rooms revenue in each year of the forecast. Income tax rate is 35%. Other expense information for year 1 and proportion or increase in forecast is projected to be as below: Account Rooms Food and Beverage Other Operated Department Administrative & General Franchise Fees† Property Operation & Maintenance Utilities Sales & Marketing Rent Property and Other Taxes Insurance Depreciation & Amortization Management Fees Amount in Year 1 25% of Rooms Revenue 60% of F&B Revenue 20% of Other Op. Dept. Rev. 10% of Total Revenue 6% of Rooms Revenue 4% of Total Revenue 3% of Total Revenue 9% of Total Revenue 1% of Total Revenue 3% of Total Revenue 1% of Total Revenue 1% of Total Revenue 2% of Total Revenue & 5% of Total GOP Proportion or Increase in Forecast 25% of Rooms Revenue Each Year (P)* 60% of F&B Revenue Each Year (P) 20% of Other Op. Dept. Rev. Each Year (P) 4% compounded annually (I)** 6% of Rooms Revenue Each Year (P) 4% compounded*** annually (I) 4% compounded annually (I) 4% compounded annually (I) 3% compounded annually (I) 3% compounded annually (I) 1% of Total Revenue Each Year (P) Remains the same 2% of Total Revenue & 5% of Total GOP Each Year (P) *Note: (P) represents ‘proportion’. **Note: (I) represents ‘increase’. ***Note: ‘compounded annually’ means that if the increase is 4%, for example, then each year’s expense is 4% larger than the previous year’s expense. †Note: Report ‘Franchise Fees’ separately from ‘Sales & Marketing’ FINANCING 1. 2. Loan-to-Value Ratio is 60%. The loan is for 20 years with the interest rate of 12%, compounded monthly. (Tip: PVIFA (1%, 240) = 90.8194) 2 [General Tips]  Figure out room number of your hotel, total project cost, and overall ADR for year 1, correctly using your own student ID number as instructed.  For your financing, you have to use the total project cost (i.e., value) and loan-to-value ratio to figure out how much you have to borrow at the beginning of the project (i.e., the beginning balance of your amortization table).  Interest expense: In your amortization table, you will have monthly interest payment for 20 years. Then, you have to calculate each year's total interest payment (by summing up interest payments for 12 months of each year) and report it on the income statement.  Depreciation expense will remain the same in dollar amount from the first year to the 10th year. 3 Loan-to-Value Ratio • Let’s assume that you are planning to develop a hotel that will cost you $10 million. If the loan-to-value ratio is 70%, how much will you borrow? – $10 million x 70% = $7 million – You have to come up with $3 million. Income Statement Format This is an example when the last two digits of student ID is 7 and 9 (student ID: 912345679). 1. You need to specify your last two digits of student ID, total number of rooms, total cost, amount of money you borrow, and day open a year. 2. P&L needs to include 10 years of projection (2018 – 2027) READING 9 TIME VALUE OF MONEY 1. What is Time Value of Money (TVM)? Time Value of Money (TVM) is an important concept in financial management. It can be used to compare investment alternatives and to solve problems involving loans, mortgages, leases, savings, and annuities. TVM is based on the concept that a dollar that you have today is worth more than the promise or expectation that you will receive a dollar in the future. Money that you hold today is worth more that money you hold in the future because you can invest it and earn interest. In other words, value of $1 today is worth more than value of $1 in the future, for example, in year 1. After all, you should receive some compensation for foregoing spending. This is called the opportunity cost, that is, the opportunity that you give up from making a certain decision (e.g., an investment). For example, by investing in a certain financial instrument, you are giving up an opportunity of enjoying a purchase of a new car. You need certain compensations for such opportunity that you give up and that can be translated into interest or return. For a numerical example, you can invest $100 for one year at a 6% annual interest rate and accumulate $106 at the end of the year. You can say that the future value of the $100 is $106 given a 6% interest rate and a one-year period. It also follows that the present value of the $106 you expect to receive in one year is only $100. A key concept of TVM is that a single sum of money or a series of equal, evenly-spaced payments or receipts promised in the future can be converted to an equivalent value today (called, Present Value). Conversely, you can determine the value to which a single sum or a series of future payments will grow to at some future date (called, Future Value). You can calculate the fourth value if you are given any three of: Interest Rate, Number of Periods, Payments, and Present or Future Value. Interest Rate Interest is a charge for borrowing money, usually stated as a percentage of the amount borrowed over a specific period of time. Interest rate includes two things: 1) opportunity cost, and 2) inflation. Simple interest is computed only on the original amount borrowed. It is the return on that principal for one time period. In contrast, compound interest is calculated each period on the original amount borrowed plus all unpaid interest accumulated to date. Compound interest is always assumed in TVM problems. Number of Periods Periods are evenly-spaced intervals of time. They are intentionally not stated in years since each interval must correspond to a compounding period for a single amount or a payment period for an annuity. A compounding period can be any period, such as a year, semi-year, quarter, month, or day. Payments Payments are a series of equal, evenly-spaced cash flows. In TVM applications, payments must represent all outflows (negative amount) or all inflows (positive amount). If you receive 1 payments, those are inflows (positive amount) and if you make payments, those are outflows (negative amount). Present Value Present Value is an amount today that is equivalent to a future payment, or series of payments, that has been discounted by an appropriate interest rate. The future amount can be a single sum that will be received at the end of the last period, as a series of equally-spaced payments (an annuity), or both. Since money has time value, the present value of a promised future amount is worth less the longer you have to wait to receive it. Future Value Future Value is the amount of money that an investment with a fixed, compounded interest rate will grow to by some future date. The investment can be a single sum deposited at the beginning of the first period, a series of equally-spaced payments (an annuity), or both. Since money has time value, we naturally expect the future value to be greater than the present value. The difference between the two depends on the number of compounding periods involved and the going interest rate. 2. Simple Future Value The first TVM concept to be presented is how to calculate the future value of a lump sum or an individual cash flow. In other words, what is a certain sum of money worth in the future at a particular rate of interest? An example would be that you deposit $1,000 into a bank account today that pays 5% interest annually. In this case, $1,000 is a lump sum or an individual cash flow which represents present value (PV), and 0 represents today. The timelines presented below often helps us understand the problem clearly. One year from today, the bank account will have a balance of $1,000 plus interest earned over that one year. Since the interest rate is 5%, you will earn $50 (5% of $1,000 = $1,000×0.05). Thus, the balance of the account after one year will be $1,050 ($1,000 + $50). This can be depicted as follows: FV1 = $1,000 × (1 + 0.05)1. If we decide to keep the money in the account for another year and earn another 5% interest for the second year, the balance will grow to $1,102.50 (= $1,050 + $52.50; $52.50 = 5% of $1,050 = $1,050×0.05). This can be depicted as follows: FV2 = $1,000 × (1 + 0.05)2. 2 The general calculation of the future value can be formularized as follows: FVn = PV × (1 + i)n, where FV represents the future value; PV represents the present value; i represents the interest rate, and n represents the number of periods between the future value and the present value. As can be seen from the example above, the interest is compounded, meaning that you earn interest on interest; for the second year, you earn 5% interest not only on $1,000 (original deposit), but also on $50 (interest income from the previous period – Year1). In this course, we use ‘Time Value of Money Tables’ to calculate the future value (and other values). The tables are designed to save the user from working through the mathematics, using the formula. For this type of problem, the table provides a factor that we multiply by the known present value to solve for the future value. Because we are solving for a future value, the factor is called a future value interest factor (FVIF). FVIFi,n is equal to (1 + i)n, so that the equation of FVn = PV × (1 + i)n can be written as FVn = PV × (FVIFi,n); (FVIFi,n) is the FVIF for a given interest rate (i) and a given number of periods (n). To solve the preceding problem using ‘Time Value of Money Tables’ (specifically ‘Simple Future Value Table’) we can write the equation as FV2 = $1,000 × (FVIF5%,2). From ‘Simple Future Value Table’ (Appendix), we can find FVIF, using the two given information; 5% of interest rate (i) and 2 of time periods (n). Each row of the table represents the number of periods while each column represents the interest rate. Therefore, we find the intersection of 5% of i in columns and 2 of n in rows, which shows 1.1025 as FVIF. Thus, by inputting 1.1025 into the equation, FV2 = $1,000 × 1.1025, we can calculate the future value of $1,102.50. 3. Simple Present Value Now, we know the future value and want to calculate the present value. We will explain the concept with an example. What is $1,320 worth today at a 10% annual interest rate? In other words, how much do you have to invest today at a 10% annual interest rate to receive $1,320 after one year. We call the process of calculating the present value of a future value, discounting. We can visualize this problem set as below. First, this problem can be solved using the following equation: 3 PV = FVn / (1 + i)n = $1,320 / (1 + 10%)1 = $1,200 Using ‘Simple Present Value Table’, we can write the equation as PV = FVn × (PVIFi,n) = $1,320 × (PVIF10%,1) = $1,320 × 0.9091 = $1,200 (PVIFi,n) is equal to 1 / (1 + i)n. (PVIF10%,1) can be found from ‘Simple Present Value Table’ by looking at the intersection of 10% of interest rate (i) in columns and 1 of time period (n) in rows – 0.9091. 4. Annuity Up to this point, we calculated the future and present value of a single lump sum, but now we are going to find the future value of a series of payments called annuity payments. An annuity is defined as a series of payments of a fixed amount for a specified number of periods of equal length. In other words, if there is the same amount of payment more than once over the same length of interval, that entire cash flow is considered as an annuity. For example, if you deposit $1,000 every year for 5 years, the entire cash flow is considered as an annuity; the same amount of payments of $1,000 and the length of interval is a year. The timelines of this example can be drawn as below: If the third year’s deposit changes to $2,000, there is no longer one annuity, but are two annuities. Examples of an annuity in our daily lives include the car payments you make to pay off a car loan, the mortgage payments made to pay off a home mortgage, or even the lease payments you make on an apartment rental to fulfill a rent contract. Of course, these examples call for monthly payments (that is, compounding period is a month), but for the time being we will look at solving problems with annual payments (that is, compounding period is a year). Later, we will deal with monthly payments or other periodic payments (that is, compounding periods other than annual). There are two types of annuity: 1) an ordinary annuity, and 2) an annuity due. In this course, we will consider only ‘an ordinary annuity.’ For an ordinary annuity, each payment or cash flow 4 happens at the end of each time period. In other words, the first payment happens at the end of the first time period, the second payment happens at the end of the second time periods, and so on, thus the last payment happens at the end of the last time period. In such case, the timeline of the entire annuity begins one period ahead of the first payment and ends at the last payment. For the example of the 5-year with $1,000 deposit, if we see this annuity as an ordinary annuity, we can find out the beginning and ending lines of the annuity as below. This ordinary annuity begins at year 0 and ends at year 5. We can determine the number of time period (n) of this ordinary annuity, using either of the following two methods. First, it is the number of payments – so, you can simply count them. For the example, there are five payments of $1,000, thus the number of time periods of the annuity (n) is five. The second method is to use the beginning and ending lines; n = Ending Year – Beginning Year. So, for the example, n is 5 (= 5 – 0). It is often easy to count the number of payments with relatively a small number of payments, such as the above example. However, if we have to deal with a large number of payments, such as a fixed amount of annual investment from your 23rd birthday to 65th birthday, or monthly payments for 30 years (i.e., a 30-year mortgage payment), the second method will be very useful. Knowing the correct beginning and ending lines is critical to calculate the future and present values of an annuity. It is because when we apply the future value concept to an annuity, we basically calculate the value of the entire annuity at the ending line. For the example above, we will be calculating the value of the entire annuity (including all five $1,000s over the five years) at the end of Year 5. When we apply the present value concept to an annuity, we basically calculate the value of the entire annuity at the beginning line. For the example above, we will be calculating the value of the entire annuity at Year 0. Now, we will show how to calculate the future and present values of an annuity (i.e., an ordinary annuity). 5. Future Value of an Annuity Let’s consider the following example to illustrate the future value of an annuity. If you deposit $50,000 at the end of each year for the next four years, earning 10% annual interest, what will be the value of your account at the end of Year 4? First, let’s draw the timeline of this example. 5 We can first determine that the entire cash flow is an annuity. Second, we will consider this annuity as an ordinary annuity (because in this course, we will consider all annuities as an ordinary annuity), we can draw the beginning line of the annuity at Year 0 and the ending line at Year 4. Now, our concern is to calculate the value of the annuity at the end of Year 4 (that is, future value of the annuity). That is one of the two things that we can calculate by using the annuity concept; again, we can calculate the value of the entire annuity either at the beginning line (when we apply the present value concept) or ending line (when we apply the future value concept). Thus, if we apply the future value concept to this annuity, we can solve the problem. Using ‘Time Value of Money Table’ (specifically, ‘Future Value of an Ordinary Annuity Table’) and the following formula, we can accomplish the goal. The formula is FVAn = PMT × (FVIFAi,n) where FVAn represents the future value of an annuity at the time period of n; PMT represents the payment per period, and (FVIFAi,n) represents the future value interest factor of an annuity from the table, using the interest rate of i and the number of time period of n. Now, using this formula and the table, we can solve the future value of the annuity of the example as follows: FVA4 = $50,000 × (FVIFA10%,4) = $50,000 × 4.6410 = $232,050 Thus, the future value of this annuity at Year 4 is $232,050. 6. Present Value of an Annuity Now, we calculate the present value of an annuity. Let’s say that you plan to withdraw $1,000 annually from an account at the end of each of the next five years. If the account pays 12% interest annually, what must you deposit today to have just enough to cover the five withdrawals? This can be viewed on a timeline as follows. 6 The timeline shows five annual payments of $1,000 each which consists of an ordinary annuity and “FVA=?” indicates we are looking for the present value of this annuity including all five payments. The beginning line of this ordinary annuity is Year 0 and the ending line is Year 5. Therefore, when we apply the present value concept to this annuity, we calculate the value of the entire annuity at the beginning line which happens to be Year 0. Now, we use the following formula to solve the problem. PVAn = PMT × (PVIFAi,n) where PVAn represents the present value of an annuity at the time period of n; PMT represents the payment per period, and (PVIFAi,n) represents the present value interest factor of an annuity from the table, using the interest rate of i and the number of time period of n. By plugging numbers in this formula, we can solve the problem. PVA5 = $1,000 × (PVIFA12%,5) = $1,000 × 3.6048 = $3,604.80 Thus, the present value of this annuity (at Year 0) is $3,604.80. 7. Future Value of a Deferred Annuity Now, let’s consider the following example. Suppose that you would like to make an investment of $3,000 annually starting at the end of year 1 for next 10 years (10 investments) at 12% return rate. Then, put the entire money into a safer investment for additional 10 years at 8% return rate. What will the future value of this investment at the end of year 20? Let’s visualize this on a timeline. Now, we have to realize that we cannot calculate the future value of this annuity at Year 20 with one step. It is because, by using the annuity concept, we can calculate the value of this annuity at only two time periods, beginning (Year 10 in this case) and ending lines (Year 10 in this case). 7 In such case, we can achieve the ultimate goal of this problem (that is, to calculate the future value at Year 20) with two steps. Those two steps are visualized on the timeline below. With the first step, we can calculate the future value of the annuity at Year 10 (which is the ending line of the annuity). Then, we will have one lump sum value of the annuity at Year 10. Once we figure out such value, then we can calculate the simple future value of such one lump sum at Year 20 which is the second step. Therefore, in the first step, we use the future value of an annuity concept with the formula of FVAn = PMT × (FVIFAi,n), then in the second step, we use the simple future value concept with the formula of FVn = PV × (FVIFi,n). Let’s see how the calculations can be done. First, the annuity has $3,000 of PMT for each year for 10 years and the interest rate is 12%. By plugging these numbers into the formula, we can calculate the future value of this annuity at the ending line of this annuity (which is, again, Year 10): FVA10 = $3,000 × (FVIFA12%,10) = $3,000 × 17.5487 = $52,646.10. Let’s see this on the timeline. Now, we took care of the annuity part, and have one lump sum of $52,646.10 at Year 10. With the second step, we can calculate the future value of this one lump sum at Year 20 which is the solution of this problem. For the second investment (from Year 10 to Year 20), the number of time period is 10 (n) and the interest rate is 8% (i); FV10 = $52,646.10 × (FVIF8%,10) = $52,646.10 × 2.1589 = $113,658.98. So, the solution is $113,658.98. We have to understand that the second part of this problem (that is, the second investment), the timeline begins at Year 10 and ends at Year 20. The second investment does not concern Year 0 to Year 10. Therefore, FV10 represents the future value at the tenth year from the beginning of this part (which is Year 10, not Year 0). So, FV10 means the future value at Year 20. In the same vein, PV in the second investment is the value at Year 10, not Year 0. So, PV is $52,646.10. When we need two steps to solve the problem for an annuity, we call it a deferred annuity. 8 8. Present Value of a Deferred Annuity Now, let’s try to calculate the present value of a deferred annuity. Suppose there is an investment that promises to pay you $100 annually beginning at the end of year 5 and continuing until the end of year 10. If you decide 7 percent is an appropriate rate of return, what is the present value of these cash flows? The timeline for this problem can be drawn as below. Now, we have to realize that we cannot calculate the present value of this annuity at Year 0 with one step. It is because, by using the annuity concept, we can calculate the value of this annuity at only two time periods, beginning (Year 4 in this case) and ending lines (Year 10 in this case). In such case, we can achieve the ultimate goal of this problem (that is, to calculate the value at Year 0) with two steps. Those two steps are visualized on the timeline below. With the first step, we can calculate the present value of the annuity at Year 4 (which is the beginning line of the annuity). Then, we will have one lump sum value of the annuity at Year 4. Once we figure out such value, then we can calculate the simple present value of such one lump sum at Year 0 which is the second step. Therefore, in the first step, we use the present value of an annuity concept with the formula of PVAn = PMT × (PVIFAi,n), then in the second step, we use the simple present value concept with the formula of PVn = FV × (PVIFi,n). Let’s see how the calculations can be done. First, the annuity has $100 of PMT for each year for 6 years and the interest rate is 7%. By plugging these numbers into the formula, we can calculate the present value of this annuity at the ending line of this annuity (which is, again, Year 4): PVA4 = $100 × (PVIFA7%,6) = $100 × 4.7665 = $476.65. Let’s see this on the timeline. 9 Now, we took care of the annuity part, and have one lump sum of $476.65 at Year 4. With the second step, we can calculate the present value of this one lump sum at Year 0 which is the solution of this problem. For the second part (from Year 4 to Year 0), the number of time period is 4 (n) and the interest rate is still 7% (i); PV0 = $476.65 × (PVIF7%,4) = $476.65 × 0.7629 = $363.64. So, the solution is $363.64. In other words, if you invest $363.64 today and earn 7% annually, then you will be able to withdraw $100 from Year 5 to Year 10, annually. 9. When Payment is Unknown Basically, to this point, we tried to calculate either future value or present value of a time value of money problem. In this section, we discuss a case where we have three values available (Interest Rate, Number of Periods, and Present or Future Value) and thus figure out the fourth value of Payments. Let’s suppose that you are planning to buy a computer for $2,000 on a loan. You have to make monthly payments for one year with the annual interest rate of 12%, compounded monthly. The first payment starts at the end of the first month. How much do you have to pay per month? We can draw the timeline as below. In this case, we know three values: present value of $2,000, interest rate of 1% (12% / 12 months), and the number of compounding periods of 12 (= 12 months). Then, we should be able to figure out the fourth value, payments (PMT). Clearly, these payments form an ordinary annuity and the present value of the annuity is $2,000. Therefore, by applying the present value concept to this annuity, we can solve the problem as follows: PVA = PMT × (PVIFAi,n) $2,000 = PMT × (PVIFA1%, 12) $2,000 = PMT × 11.2551 Then, divide the both sides by 11.2551; $2,000 / 11.2551 = (PMT × 11.2551) / 11.2551 Then, PMT = $2,000 / 11.2551 = $177.70 (monthly payment) 10 Now, we can construct a table called, ‘Amortization Table’ of this loan payment. [Amortization Table] Month Payment 0 1 177.70 2 177.70 3 177.70 4 177.70 5 177.70 6 177.70 7 177.70 8 177.70 9 177.70 10 177.70 11 177.70 12 177.70 Total 2132.40 Interest 20 18.42 16.83 15.22 13.60 11.96 10.30 8.62 6.93 5.23 3.50 1.76 132.371 Principal 157.70 159.28 160.87 162.48 164.10 165.74 167.40 169.08 170.77 172.47 174.20 175.94 2000 Balance 2000 1842.30 1683.02 1522.15 1359.67 1195.57 1029.83 862.43 693.35 522.58 350.11 175.91 0 (-0.03) First, the balance starts as $2,000 today (Month 0). Then, after the first month, you make the first monthly payment of $177.70 as calculated before. This monthly payment incurs for every month for the entire period of 12 months, and consists of two components: interest payment and principal payment. Interest payment is calculated by multiplying the balance by the interest rate per compounding period. Thus, for the first month, the interest payment is calculated by the balance of $2,000 by the interest rate of 1% per month; $20 = $2,000 × 1%. After the bank takes this interest payment of $20 out of the monthly payment of $177.70, the remaining portion of the monthly payment is $157.70 (= $177.70 – $20) that is called ‘Principal Payment’. This principal payment reduces the balance, thus the balance after the first month becomes $1,842.30 (= $2,000 – $157.70). After the second month, you make another monthly payment of $177.70. The interest payment for the second month is calculated by multiplying the balance of $1,842.30 by the interest rate per month of 1% = $18.42. The principal payment is calculated after taking the interest payment ($18.42) from the monthly payment ($177.70); $159.28 (=$177.70 – $18.42). The same procedure is repeated for the remaining 10 months. After making the last monthly payment, the balance should become zero. In the table above, the final balance is -$0.03, not exactly $0, just because the monthly payment used in this problem is a round-up value. 11 APPENDIX [Simple Future Value Table] N 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 1% 1.0100 1.0201 1.0303 1.0406 1.0510 1.0615 1.0721 1.0829 1.0937 1.1046 1.1157 1.1268 1.1381 1.1495 1.1610 1.1726 1.1843 1.1961 1.2081 1.2202 1.2324 1.2447 1.2572 1.2697 1.2824 1.2953 1.3082 1.3213 1.3345 1.3478 1.3613 1.3749 1.3887 1.4026 1.4166 1.4308 1.4451 1.4595 1.4741 1.4889 1.5038 1.5188 1.5340 1.5493 1.5648 1.5805 1.5963 1.6122 1.6283 1.6446 2% 1.0200 1.0404 1.0612 1.0824 1.1041 1.1262 1.1487 1.1717 1.1951 1.2190 1.2434 1.2682 1.2936 1.3195 1.3459 1.3728 1.4002 1.4282 1.4568 1.4859 1.5157 1.5460 1.5769 1.6084 1.6406 1.6734 1.7069 1.7410 1.7758 1.8114 1.8476 1.8845 1.9222 1.9607 1.9999 2.0399 2.0807 2.1223 2.1647 2.2080 2.2522 2.2972 2.3432 2.3901 2.4379 2.4866 2.5363 2.5871 2.6388 2.6916 3% 1.0300 1.0609 1.0927 1.1255 1.1593 1.1941 1.2299 1.2668 1.3048 1.3439 1.3842 1.4258 1.4685 1.5126 1.5580 1.6047 1.6528 1.7024 1.7535 1.8061 1.8603 1.9161 1.9736 2.0328 2.0938 2.1566 2.2213 2.2879 2.3566 2.4273 2.5001 2.5751 2.6523 2.7319 2.8139 2.8983 2.9852 3.0748 3.1670 3.2620 3.3599 3.4607 3.5645 3.6715 3.7816 3.8950 4.0119 4.1323 4.2562 4.3839 4% 1.0400 1.0816 1.1249 1.1699 1.2167 1.2653 1.3159 1.3686 1.4233 1.4802 1.5395 1.6010 1.6651 1.7317 1.8009 1.8730 1.9479 2.0258 2.1068 2.1911 2.2788 2.3699 2.4647 2.5633 2.6658 2.7725 2.8834 2.9987 3.1187 3.2434 3.3731 3.5081 3.6484 3.7943 3.9461 4.1039 4.2681 4.4388 4.6164 4.8010 4.9931 5.1928 5.4005 5.6165 5.8412 6.0748 6.3178 6.5705 6.8333 7.1067 5% 1.0500 1.1025 1.1576 1.2155 1.2763 1.3401 1.4071 1.4775 1.5513 1.6289 1.7103 1.7959 1.8856 1.9799 2.0789 2.1829 2.2920 2.4066 2.5270 2.6533 2.7860 2.9253 3.0715 3.2251 3.3864 3.5557 3.7335 3.9201 4.1161 4.3219 4.5380 4.7649 5.0032 5.2533 5.5160 5.7918 6.0814 6.3855 6.7048 7.0400 7.3920 7.7616 8.1497 8.5572 8.9850 9.4343 9.9060 10.4013 10.9213 11.4674 6% 1.0600 1.1236 1.1910 1.2625 1.3382 1.4185 1.5036 1.5938 1.6895 1.7908 1.8983 2.0122 2.1329 2.2609 2.3966 2.5404 2.6928 2.8543 3.0256 3.2071 3.3996 3.6035 3.8197 4.0489 4.2919 4.5494 4.8223 5.1117 5.4184 5.7435 6.0881 6.4534 6.8406 7.2510 7.6861 8.1473 8.6361 9.1543 9.7035 10.2857 10.9029 11.5570 12.2505 12.9855 13.7646 14.5905 15.4659 16.3939 17.3775 18.4202 7% 1.0700 1.1449 1.2250 1.3108 1.4026 1.5007 1.6058 1.7182 1.8385 1.9672 2.1049 2.2522 2.4098 2.5785 2.7590 2.9522 3.1588 3.3799 3.6165 3.8697 4.1406 4.4304 4.7405 5.0724 5.4274 5.8074 6.2139 6.6488 7.1143 7.6123 8.1451 8.7153 9.3253 9.9781 10.6766 11.4239 12.2236 13.0793 13.9948 14.9745 16.0227 17.1443 18.3444 19.6285 21.0025 22.4726 24.0457 25.7289 27.5299 29.4570 12 8% 1.0800 1.1664 1.2597 1.3605 1.4693 1.5869 1.7138 1.8509 1.9990 2.1589 2.3316 2.5182 2.7196 2.9372 3.1722 3.4259 3.7000 3.9960 4.3157 4.6610 5.0338 5.4365 5.8715 6.3412 6.8485 7.3964 7.9881 8.6271 9.3173 10.0627 10.8677 11.7371 12.6760 13.6901 14.7853 15.9682 17.2456 18.6253 20.1153 21.7245 23.4625 25.3395 27.3666 29.5560 31.9204 34.4741 37.2320 40.2106 43.4274 46.9016 9% 1.0900 1.1881 1.2950 1.4116 1.5386 1.6771 1.8280 1.9926 2.1719 2.3674 2.5804 2.8127 3.0658 3.3417 3.6425 3.9703 4.3276 4.7171 5.1417 5.6044 6.1088 6.6586 7.2579 7.9111 8.6231 9.3992 10.2451 11.1671 12.1722 13.2677 14.4618 15.7633 17.1820 18.7284 20.4140 22.2512 24.2538 26.4367 28.8160 31.4094 34.2363 37.3175 40.6761 44.3370 48.3273 52.6767 57.4176 62.5852 68.2179 74.3575 10% 1.1000 1.2100 1.3310 1.4641 1.6105 1.7716 1.9487 2.1436 2.3579 2.5937 2.8531 3.1384 3.4523 3.7975 4.1772 4.5950 5.0545 5.5599 6.1159 6.7275 7.4002 8.1403 8.9543 9.8497 10.8347 11.9182 13.1100 14.4210 15.8631 17.4494 19.1943 21.1138 23.2252 25.5477 28.1024 30.9127 34.0039 37.4043 41.1448 45.2593 49.7852 54.7637 60.2401 66.2641 72.8905 80.1795 88.1975 97.0172 106.7190 117.3909 11% 1.1100 1.2321 1.3676 1.5181 1.6851 1.8704 2.0762 2.3045 2.5580 2.8394 3.1518 3.4985 3.8833 4.3104 4.7846 5.3109 5.8951 6.5436 7.2633 8.0623 8.9492 9.9336 11.0263 12.2392 13.5855 15.0799 16.7386 18.5799 20.6237 22.8923 25.4104 28.2056 31.3082 34.7521 38.5749 42.8181 47.5281 52.7562 58.5593 65.0009 72.1510 80.0876 88.8972 98.6759 109.5302 121.5786 134.9522 149.7970 166.2746 184.5648 12% 1.1200 1.2544 1.4049 1.5735 1.7623 1.9738 2.2107 2.4760 2.7731 3.1058 3.4785 3.8960 4.3635 4.8871 5.4736 6.1304 6.8660 7.6900 8.6128 9.6463 10.8038 12.1003 13.5523 15.1786 17.0001 19.0401 21.3249 23.8839 26.7499 29.9599 33.5551 37.5817 42.0915 47.1425 52.7996 59.1356 66.2318 74.1797 83.0812 93.0510 104.2171 116.7231 130.7299 146.4175 163.9876 183.6661 205.7061 230.3908 258.0377 289.0022 13% 1.1300 1.2769 1.4429 1.6305 1.8424 2.0820 2.3526 2.6584 3.0040 3.3946 3.8359 4.3345 4.8980 5.5348 6.2543 7.0673 7.9861 9.0243 10.1974 11.5231 13.0211 14.7138 16.6266 18.7881 21.2305 23.9905 27.1093 30.6335 34.6158 39.1159 44.2010 49.9471 56.4402 63.7774 72.0685 81.4374 92.0243 103.9874 117.5058 132.7816 150.0432 169.5488 191.5901 216.4968 244.6414 276.4448 312.3826 352.9923 398.8813 450.7359 [Simple Present Value Table] N 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 1% 0.9901 0.9803 0.9706 0.9610 0.9515 0.9420 0.9327 0.9235 0.9143 0.9053 0.8963 0.8874 0.8787 0.8700 0.8613 0.8528 0.8444 0.8360 0.8277 0.8195 0.8114 0.8034 0.7954 0.7876 0.7798 0.7720 0.7644 0.7568 0.7493 0.7419 0.7346 0.7273 0.7201 0.7130 0.7059 0.6989 0.6920 0.6852 0.6784 0.6717 0.6650 0.6584 0.6519 0.6454 0.6391 0.6327 0.6265 0.6203 0.6141 0.6080 2% 0.9804 0.9612 0.9423 0.9238 0.9057 0.8880 0.8706 0.8535 0.8368 0.8203 0.8043 0.7885 0.7730 0.7579 0.7430 0.7284 0.7142 0.7002 0.6864 0.6730 0.6598 0.6468 0.6342 0.6217 0.6095 0.5976 0.5859 0.5744 0.5631 0.5521 0.5412 0.5306 0.5202 0.5100 0.5000 0.4902 0.4806 0.4712 0.4619 0.4529 0.4440 0.4353 0.4268 0.4184 0.4102 0.4022 0.3943 0.3865 0.3790 0.3715 3% 0.9709 0.9426 0.9151 0.8885 0.8626 0.8375 0.8131 0.7894 0.7664 0.7441 0.7224 0.7014 0.6810 0.6611 0.6419 0.6232 0.6050 0.5874 0.5703 0.5537 0.5375 0.5219 0.5067 0.4919 0.4776 0.4637 0.4502 0.4371 0.4243 0.4120 0.4000 0.3883 0.3770 0.3660 0.3554 0.3450 0.3350 0.3252 0.3158 0.3066 0.2976 0.2890 0.2805 0.2724 0.2644 0.2567 0.2493 0.2420 0.2350 0.2281 4% 0.9615 0.9246 0.8890 0.8548 0.8219 0.7903 0.7599 0.7307 0.7026 0.6756 0.6496 0.6246 0.6006 0.5775 0.5553 0.5339 0.5134 0.4936 0.4746 0.4564 0.4388 0.4220 0.4057 0.3901 0.3751 0.3607 0.3468 0.3335 0.3207 0.3083 0.2965 0.2851 0.2741 0.2636 0.2534 0.2437 0.2343 0.2253 0.2166 0.2083 0.2003 0.1926 0.1852 0.1780 0.1712 0.1646 0.1583 0.1522 0.1463 0.1407 5% 0.9524 0.9070 0.8638 0.8227 0.7835 0.7462 0.7107 0.6768 0.6446 0.6139 0.5847 0.5568 0.5303 0.5051 0.4810 0.4581 0.4363 0.4155 0.3957 0.3769 0.3589 0.3418 0.3256 0.3101 0.2953 0.2812 0.2678 0.2551 0.2429 0.2314 0.2204 0.2099 0.1999 0.1904 0.1813 0.1727 0.1644 0.1566 0.1491 0.1420 0.1353 0.1288 0.1227 0.1169 0.1113 0.1060 0.1009 0.0961 0.0916 0.0872 6% 0.9434 0.8900 0.8396 0.7921 0.7473 0.7050 0.6651 0.6274 0.5919 0.5584 0.5268 0.4970 0.4688 0.4423 0.4173 0.3936 0.3714 0.3503 0.3305 0.3118 0.2942 0.2775 0.2618 0.2470 0.2330 0.2198 0.2074 0.1956 0.1846 0.1741 0.1643 0.1550 0.1462 0.1379 0.1301 0.1227 0.1158 0.1092 0.1031 0.0972 0.0917 0.0865 0.0816 0.0770 0.0727 0.0685 0.0647 0.0610 0.0575 0.0543 7% 0.9346 0.8734 0.8163 0.7629 0.7130 0.6663 0.6227 0.5820 0.5439 0.5083 0.4751 0.4440 0.4150 0.3878 0.3624 0.3387 0.3166 0.2959 0.2765 0.2584 0.2415 0.2257 0.2109 0.1971 0.1842 0.1722 0.1609 0.1504 0.1406 0.1314 0.1228 0.1147 0.1072 0.1002 0.0937 0.0875 0.0818 0.0765 0.0715 0.0668 0.0624 0.0583 0.0545 0.0509 0.0476 0.0445 0.0416 0.0389 0.0363 0.0339 13 8% 0.9259 0.8573 0.7938 0.7350 0.6806 0.6302 0.5835 0.5403 0.5002 0.4632 0.4289 0.3971 0.3677 0.3405 0.3152 0.2919 0.2703 0.2502 0.2317 0.2145 0.1987 0.1839 0.1703 0.1577 0.1460 0.1352 0.1252 0.1159 0.1073 0.0994 0.0920 0.0852 0.0789 0.0730 0.0676 0.0626 0.0580 0.0537 0.0497 0.0460 0.0426 0.0395 0.0365 0.0338 0.0313 0.0290 0.0269 0.0249 0.0230 0.0213 9% 0.9174 0.8417 0.7722 0.7084 0.6499 0.5963 0.5470 0.5019 0.4604 0.4224 0.3875 0.3555 0.3262 0.2992 0.2745 0.2519 0.2311 0.2120 0.1945 0.1784 0.1637 0.1502 0.1378 0.1264 0.1160 0.1064 0.0976 0.0895 0.0822 0.0754 0.0691 0.0634 0.0582 0.0534 0.0490 0.0449 0.0412 0.0378 0.0347 0.0318 0.0292 0.0268 0.0246 0.0226 0.0207 0.0190 0.0174 0.0160 0.0147 0.0134 10% 0.9091 0.8264 0.7513 0.6830 0.6209 0.5645 0.5132 0.4665 0.4241 0.3855 0.3505 0.3186 0.2897 0.2633 0.2394 0.2176 0.1978 0.1799 0.1635 0.1486 0.1351 0.1228 0.1117 0.1015 0.0923 0.0839 0.0763 0.0693 0.0630 0.0573 0.0521 0.0474 0.0431 0.0391 0.0356 0.0323 0.0294 0.0267 0.0243 0.0221 0.0201 0.0183 0.0166 0.0151 0.0137 0.0125 0.0113 0.0103 0.0094 0.0085 11% 0.9009 0.8116 0.7312 0.6587 0.5935 0.5346 0.4817 0.4339 0.3909 0.3522 0.3173 0.2858 0.2575 0.2320 0.2090 0.1883 0.1696 0.1528 0.1377 0.1240 0.1117 0.1007 0.0907 0.0817 0.0736 0.0663 0.0597 0.0538 0.0485 0.0437 0.0394 0.0355 0.0319 0.0288 0.0259 0.0234 0.0210 0.0190 0.0171 0.0154 0.0139 0.0125 0.0112 0.0101 0.0091 0.0082 0.0074 0.0067 0.0060 0.0054 12% 0.8929 0.7972 0.7118 0.6355 0.5674 0.5066 0.4523 0.4039 0.3606 0.3220 0.2875 0.2567 0.2292 0.2046 0.1827 0.1631 0.1456 0.1300 0.1161 0.1037 0.0926 0.0826 0.0738 0.0659 0.0588 0.0525 0.0469 0.0419 0.0374 0.0334 0.0298 0.0266 0.0238 0.0212 0.0189 0.0169 0.0151 0.0135 0.0120 0.0107 0.0096 0.0086 0.0076 0.0068 0.0061 0.0054 0.0049 0.0043 0.0039 0.0035 13% 0.8850 0.7831 0.6931 0.6133 0.5428 0.4803 0.4251 0.3762 0.3329 0.2946 0.2607 0.2307 0.2042 0.1807 0.1599 0.1415 0.1252 0.1108 0.0981 0.0868 0.0768 0.0680 0.0601 0.0532 0.0471 0.0417 0.0369 0.0326 0.0289 0.0256 0.0226 0.0200 0.0177 0.0157 0.0139 0.0123 0.0109 0.0096 0.0085 0.0075 0.0067 0.0059 0.0052 0.0046 0.0041 0.0036 0.0032 0.0028 0.0025 0.0022 [Future Value of an Ordinary Annuity Table] N 1% 2% 3% 4% 5% 6% 7% 8% 9% 1 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 2 2.0100 2.0200 2.0300 2.0400 2.0500 2.0600 2.0700 2.0800 2.0900 2.1000 2.1100 2.1200 2.1300 3 3.0301 3.0604 3.0909 3.1216 3.1525 3.1836 3.2149 3.2464 3.2781 3.3100 3.3421 3.3744 3.4069 4 4.0604 4.1216 4.1836 4.2465 4.3101 4.3746 4.4399 4.5061 4.5731 4.6410 4.7097 4.7793 4.8498 5 5.1010 5.2040 5.3091 5.4163 5.5256 5.6371 5.7507 5.8666 5.9847 6.1051 6.2278 6.3528 6.4803 6 6.1520 6.3081 6.4684 6.6330 6.8019 6.9753 7.1533 7.3359 7.5233 7.7156 7.9129 8.1152 8.3227 7 7.2135 7.4343 7.6625 7.8983 8.1420 8.3938 8.6540 8.9228 9.2004 9.4872 9.7833 10.0890 10.4047 8 8.2857 8.5830 8.8923 9.2142 9.5491 9.8975 10.2598 10.6366 11.0285 11.4359 11.8594 12.2997 12.7573 9 9.3685 9.7546 10.1591 10.5828 11.0266 11.4913 11.9780 12.4876 13.0210 13.5795 14.1640 14.7757 15.4157 10 10.4622 10.9497 11.4639 12.0061 12.5779 13.1808 13.8164 14.4866 15.1929 15.9374 16.7220 17.5487 18.4197 11 11.5668 12.1687 12.8078 13.4864 14.2068 14.9716 15.7836 16.6455 17.5603 18.5312 19.5614 20.6546 21.8143 12 12.6825 13.4121 14.1920 15.0258 15.9171 16.8699 17.8885 18.9771 20.1407 21.3843 22.7132 24.1331 25.6502 13 13.8093 14.6803 15.6178 16.6268 17.7130 18.8821 20.1406 21.4953 22.9534 24.5227 26.2116 28.0291 29.9847 14 14.9474 15.9739 17.0863 18.2919 19.5986 21.0151 22.5505 24.2149 26.0192 27.9750 30.0949 32.3926 34.8827 15 16.0969 17.2934 18.5989 20.0236 21.5786 23.2760 25.1290 27.1521 29.3609 31.7725 34.4054 37.2797 40.4175 16 17.2579 18.6393 20.1569 21.8245 23.6575 25.6725 27.8881 30.3243 33.0034 35.9497 39.1899 42.7533 46.6717 17 18.4304 20.0121 21.7616 23.6975 25.8404 28.2129 30.8402 33.7502 36.9737 40.5447 44.5008 48.8837 53.7391 18 19.6147 21.4123 23.4144 25.6454 28.1324 30.9057 33.9990 37.4502 41.3013 45.5992 50.3959 55.7497 61.7251 19 20.8109 22.8406 25.1169 27.6712 30.5390 33.7600 37.3790 41.4463 46.0185 51.1591 56.9395 63.4397 70.7494 20 22.0190 24.2974 26.8704 29.7781 33.0660 36.7856 40.9955 45.7620 51.1601 57.2750 64.2028 72.0524 80.9468 21 23.2392 25.7833 28.6765 31.9692 35.7193 39.9927 44.8652 50.4229 56.7645 64.0025 72.2651 81.6987 92.4699 22 24.4716 27.2990 30.5368 34.2480 38.5052 43.3923 49.0057 55.4568 62.8733 71.4027 81.2143 92.5026 105.4910 23 25.7163 28.8450 32.4529 36.6179 41.4305 46.9958 53.4361 60.8933 69.5319 79.5430 91.1479 104.6029 120.2048 24 26.9735 30.4219 34.4265 39.0826 44.5020 50.8156 58.1767 66.7648 76.7898 88.4973 102.1742 118.1552 136.8315 25 28.2432 32.0303 36.4593 41.6459 47.7271 54.8645 63.2490 73.1059 84.7009 98.3471 114.4133 133.3339 155.6196 26 29.5256 33.6709 38.5530 44.3117 51.1135 59.1564 68.6765 79.9544 93.3240 109.1818 127.9988 150.3339 176.8501 27 30.8209 35.3443 40.7096 47.0842 54.6691 63.7058 74.4838 87.3508 102.7231 121.0999 143.0786 169.3740 200.8406 28 32.1291 37.0512 42.9309 49.9676 58.4026 68.5281 80.6977 95.3388 112.9682 134.2099 159.8173 190.6989 227.9499 29 33.4504 38.7922 45.2189 52.9663 62.3227 73.6398 87.3465 103.9659 124.1354 148.6309 178.3972 214.5828 258.5834 30 34.7849 40.5681 47.5754 56.0849 66.4388 79.0582 94.4608 113.2832 136.3075 164.4940 199.0209 241.3327 293.1992 31 36.1327 42.3794 50.0027 59.3283 70.7608 84.8017 102.0730 123.3459 149.5752 181.9434 221.9132 271.2926 332.3151 32 37.4941 44.2270 52.5028 62.7015 75.2988 90.8898 110.2182 134.2135 164.0370 201.1378 247.3236 304.8477 376.5161 33 38.8690 46.1116 55.0778 66.2095 80.0638 97.3432 118.9334 145.9506 179.8003 222.2515 275.5292 342.4294 426.4632 34 40.2577 48.0338 57.7302 69.8579 85.0670 104.1838 128.2588 158.6267 196.9823 245.4767 306.8374 384.5210 482.9034 35 41.6603 49.9945 60.4621 73.6522 90.3203 111.4348 138.2369 172.3168 215.7108 271.0244 341.5896 431.6635 546.6808 36 43.0769 51.9944 63.2759 77.5983 95.8363 119.1209 148.9135 187.1021 236.1247 299.1268 380.1644 484.4631 618.7493 37 44.5076 54.0343 66.1742 81.7022 101.6281 127.2681 160.3374 203.0703 258.3759 330.0395 422.9825 543.5987 700.1867 38 45.9527 56.1149 69.1594 85.9703 107.7095 135.9042 172.5610 220.3159 282.6298 364.0434 470.5106 609.8305 792.2110 39 47.4123 58.2372 72.2342 90.4091 114.0950 145.0585 185.6403 238.9412 309.0665 401.4478 523.2667 684.0102 896.1984 40 48.8864 60.4020 75.4013 95.0255 120.7998 154.7620 199.6351 259.0565 337.8824 442.5926 581.8261 767.0914 1013.7042 41 50.3752 62.6100 78.6633 99.8265 127.8398 165.0477 214.6096 280.7810 369.2919 487.8518 646.8269 860.1424 1146.4858 42 51.8790 64.8622 82.0232 104.8196 135.2318 175.9505 230.6322 304.2435 403.5281 537.6370 718.9779 964.3595 1296.5289 43 53.3978 67.1595 85.4839 110.0124 142.9933 187.5076 247.7765 329.5830 440.8457 592.4007 799.0655 1081.0826 1466.0777 44 54.9318 69.5027 89.0484 115.4129 151.1430 199.7580 266.1209 356.9496 481.5218 652.6408 887.9627 1211.8125 1657.6678 45 56.4811 71.8927 92.7199 121.0294 159.7002 212.7435 285.7493 386.5056 525.8587 718.9048 986.6386 1358.2300 1874.1646 46 58.0459 74.3306 96.5015 126.8706 168.6852 226.5081 306.7518 418.4261 574.1860 791.7953 1096.1688 1522.2176 2118.8060 47 59.6263 76.8172 100.3965 132.9454 178.1194 241.0986 329.2244 452.9002 626.8628 871.9749 1217.7474 1705.8838 2395.2508 48 61.2226 79.3535 104.4084 139.2632 188.0254 256.5645 353.2701 490.1322 684.2804 960.1723 1352.6996 1911.5898 2707.6334 49 62.8348 81.9406 108.5406 145.8337 198.4267 272.9584 378.9990 530.3427 746.8656 1057.1896 1502.4965 2141.9806 3060.6258 50 64.4632 84.5794 112.7969 152.6671 209.3480 290.3359 406.5289 573.7702 815.0836 1163.9085 1668.7712 2400.0182 3459.5071 14 10% 11% 12% 13% [Present Value of an Ordinary Annuity Table] N 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 1% 0.9901 1.9704 2.9410 3.9020 4.8534 5.7955 6.7282 7.6517 8.5660 9.4713 10.3676 11.2551 12.1337 13.0037 13.8651 14.7179 15.5623 16.3983 17.2260 18.0456 18.8570 19.6604 20.4558 21.2434 22.0232 22.7952 23.5596 24.3164 25.0658 25.8077 26.5423 27.2696 27.9897 28.7027 29.4086 30.1075 30.7995 31.4847 32.1630 32.8347 33.4997 34.1581 34.8100 35.4555 36.0945 36.7272 37.3537 37.9740 38.5881 39.1961 2% 0.9804 1.9416 2.8839 3.8077 4.7135 5.6014 6.4720 7.3255 8.1622 8.9826 9.7868 10.5753 11.3484 12.1062 12.8493 13.5777 14.2919 14.9920 15.6785 16.3514 17.0112 17.6580 18.2922 18.9139 19.5235 20.1210 20.7069 21.2813 21.8444 22.3965 22.9377 23.4683 23.9886 24.4986 24.9986 25.4888 25.9695 26.4406 26.9026 27.3555 27.7995 28.2348 28.6616 29.0800 29.4902 29.8923 30.2866 30.6731 31.0521 31.4236 3% 0.9709 1.9135 2.8286 3.7171 4.5797 5.4172 6.2303 7.0197 7.7861 8.5302 9.2526 9.9540 10.6350 11.2961 11.9379 12.5611 13.1661 13.7535 14.3238 14.8775 15.4150 15.9369 16.4436 16.9355 17.4131 17.8768 18.3270 18.7641 19.1885 19.6004 20.0004 20.3888 20.7658 21.1318 21.4872 21.8323 22.1672 22.4925 22.8082 23.1148 23.4124 23.7014 23.9819 24.2543 24.5187 24.7754 25.0247 25.2667 25.5017 25.7298 4% 0.9615 1.8861 2.7751 3.6299 4.4518 5.2421 6.0021 6.7327 7.4353 8.1109 8.7605 9.3851 9.9856 10.5631 11.1184 11.6523 12.1657 12.6593 13.1339 13.5903 14.0292 14.4511 14.8568 15.2470 15.6221 15.9828 16.3296 16.6631 16.9837 17.2920 17.5885 17.8736 18.1476 18.4112 18.6646 18.9083 19.1426 19.3679 19.5845 19.7928 19.9931 20.1856 20.3708 20.5488 20.7200 20.8847 21.0429 21.1951 21.3415 21.4822 5% 0.9524 1.8594 2.7232 3.5460 4.3295 5.0757 5.7864 6.4632 7.1078 7.7217 8.3064 8.8633 9.3936 9.8986 10.3797 10.8378 11.2741 11.6896 12.0853 12.4622 12.8212 13.1630 13.4886 13.7986 14.0939 14.3752 14.6430 14.8981 15.1411 15.3725 15.5928 15.8027 16.0025 16.1929 16.3742 16.5469 16.7113 16.8679 17.0170 17.1591 17.2944 17.4232 17.5459 17.6628 17.7741 17.8801 17.9810 18.0772 18.1687 18.2559 6% 0.9434 1.8334 2.6730 3.4651 4.2124 4.9173 5.5824 6.2098 6.8017 7.3601 7.8869 8.3838 8.8527 9.2950 9.7122 10.1059 10.4773 10.8276 11.1581 11.4699 11.7641 12.0416 12.3034 12.5504 12.7834 13.0032 13.2105 13.4062 13.5907 13.7648 13.9291 14.0840 14.2302 14.3681 14.4982 14.6210 14.7368 14.8460 14.9491 15.0463 15.1380 15.2245 15.3062 15.3832 15.4558 15.5244 15.5890 15.6500 15.7076 15.7619 7% 0.9346 1.8080 2.6243 3.3872 4.1002 4.7665 5.3893 5.9713 6.5152 7.0236 7.4987 7.9427 8.3577 8.7455 9.1079 9.4466 9.7632 10.0591 10.3356 10.5940 10.8355 11.0612 11.2722 11.4693 11.6536 11.8258 11.9867 12.1371 12.2777 12.4090 12.5318 12.6466 12.7538 12.8540 12.9477 13.0352 13.1170 13.1935 13.2649 13.3317 13.3941 13.4524 13.5070 13.5579 13.6055 13.6500 13.6916 13.7305 13.7668 13.8007 15 8% 0.9259 1.7833 2.5771 3.3121 3.9927 4.6229 5.2064 5.7466 6.2469 6.7101 7.1390 7.5361 7.9038 8.2442 8.5595 8.8514 9.1216 9.3719 9.6036 9.8181 10.0168 10.2007 10.3711 10.5288 10.6748 10.8100 10.9352 11.0511 11.1584 11.2578 11.3498 11.4350 11.5139 11.5869 11.6546 11.7172 11.7752 11.8289 11.8786 11.9246 11.9672 12.0067 12.0432 12.0771 12.1084 12.1374 12.1643 12.1891 12.2122 12.2335 9% 0.9174 1.7591 2.5313 3.2397 3.8897 4.4859 5.0330 5.5348 5.9952 6.4177 6.8052 7.1607 7.4869 7.7862 8.0607 8.3126 8.5436 8.7556 8.9501 9.1285 9.2922 9.4424 9.5802 9.7066 9.8226 9.9290 10.0266 10.1161 10.1983 10.2737 10.3428 10.4062 10.4644 10.5178 10.5668 10.6118 10.6530 10.6908 10.7255 10.7574 10.7866 10.8134 10.8380 10.8605 10.8812 10.9002 10.9176 10.9336 10.9482 10.9617 10% 0.9091 1.7355 2.4869 3.1699 3.7908 4.3553 4.8684 5.3349 5.7590 6.1446 6.4951 6.8137 7.1034 7.3667 7.6061 7.8237 8.0216 8.2014 8.3649 8.5136 8.6487 8.7715 8.8832 8.9847 9.0770 9.1609 9.2372 9.3066 9.3696 9.4269 9.4790 9.5264 9.5694 9.6086 9.6442 9.6765 9.7059 9.7327 9.7570 9.7791 9.7991 9.8174 9.8340 9.8491 9.8628 9.8753 9.8866 9.8969 9.9063 9.9148 11% 0.9009 1.7125 2.4437 3.1024 3.6959 4.2305 4.7122 5.1461 5.5370 5.8892 6.2065 6.4924 6.7499 6.9819 7.1909 7.3792 7.5488 7.7016 7.8393 7.9633 8.0751 8.1757 8.2664 8.3481 8.4217 8.4881 8.5478 8.6016 8.6501 8.6938 8.7331 8.7686 8.8005 8.8293 8.8552 8.8786 8.8996 8.9186 8.9357 8.9511 8.9649 8.9774 8.9886 8.9988 9.0079 9.0161 9.0235 9.0302 9.0362 9.0417 12% 0.8929 1.6901 2.4018 3.0373 3.6048 4.1114 4.5638 4.9676 5.3282 5.6502 5.9377 6.1944 6.4235 6.6282 6.8109 6.9740 7.1196 7.2497 7.3658 7.4694 7.5620 7.6446 7.7184 7.7843 7.8431 7.8957 7.9426 7.9844 8.0218 8.0552 8.0850 8.1116 8.1354 8.1566 8.1755 8.1924 8.2075 8.2210 8.2330 8.2438 8.2534 8.2619 8.2696 8.2764 8.2825 8.2880 8.2928 8.2972 8.3010 8.3045 13% 0.8850 1.6681 2.3612 2.9745 3.5172 3.9975 4.4226 4.7988 5.1317 5.4262 5.6869 5.9176 6.1218 6.3025 6.4624 6.6039 6.7291 6.8399 6.9380 7.0248 7.1016 7.1695 7.2297 7.2829 7.3300 7.3717 7.4086 7.4412 7.4701 7.4957 7.5183 7.5383 7.5560 7.5717 7.5856 7.5979 7.6087 7.6183 7.6268 7.6344 7.6410 7.6469 7.6522 7.6568 7.6609 7.6645 7.6677 7.6705 7.6730 7.6752 My student ID 915306253 *You will need this in order to do the assignment Thank You