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1. True or false. When simple interest is used, the accumulated amount is a linear function
of time.
2. True or false. Compound interest that is converted once a year is the same as simple
interest.
3. True or false. If interest is compounded annually, then the effective rate of interest is the
same as the nominal rate of interest.
4. True or false. The present value is always smaller than the future value.
5. True or false. The future value of an annuity can be found by adding together all the
payments that are paid into an account.
6. True or false. The periodic payment R where
and P is the loan amount
and i is the interest per period that will amortize the loan at the end of the term
comprising n periods.
7. True or false. A sinking fund is the accumulated amount to be realized at some future
date (the end of the term) when a fixed number of periodic payments are paid into an
account earning interest at the rate of i per period.

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Interest rates

Interest rates

Interest rates are a fact of life that you will encounter both professionally and personally. One area of interest rates that you may be most concerned about are those applied to credit card debt. Let’s say that you had $2400 on a particular credit card that charges an annual percentage rate (APR) of 21% and requires that you pay a minimum of 2% per month. Could you determine the minimum monthly payment? The minimum monthly payment would simply be 2% times the balance as shown: 2% x $2400.00 = 0.02 x $2400.00 = $48.00 So, your monthly minimum payment would be $48.00. Do you know how much of this is being applied to the principle and how much is going to interest? To determine this, you would need to know the simple interest formula. I = Prt In this formula, I = interest, P = is the principle (balance), r = is the annual percentage rate, and t is the time frame. To determine the interest per month on a balance of $2400 with an APR of 21%, you would let P = $2400, r = .21, and t = 1/12 (1 month is 1/12 of a year). The interest paid each month would then be: I = Prt = ($2400)(.21)(1/12) = $42.00 So, you are paying $42.00 per month towards interest. With a minimum payment of $48.00, that means you are paying $6.00 per month towards the balance ($48.00 - $42.00 = $6.00). No wonder it takes so long to pay off a credit card! Research interest rates and consumer debt using the Argosy University online library resources and the Internet. Based on the articles and your independent research, respond to the following: How is consumer debt different today than in the past? What role do interest rates play in mounting consumer debt? What are the typical interest rates applied to credit cards, mortgages, and other debt? Many of today’s interest rates are variable rather than fixed. What difference does this make to pension plans, housing loans, and other personal finances? Write your response in 1–2 paragraphs (a total of 200-300 words).

Population Growth

Population Growth

Population GrowthTo study the growth of a population mathematically, we use the concept of exponential models. Generally speaking, if we want to predict the increase in the population at a certain period in time, we start by considering the current population and apply an assumed annual growth rate. For example, if the U.S. population in 2008 was 301 million and the annual growth rate was 0.9%, what would be the population in the year 2050? To solve this problem, we would use the following formula:P(1 + r)nIn this formula, P represents the initial population we are considering, r represents the annual growth rate expressed as a decimal and n is the number of years of growth. In this example, P = 301,000,000, r = 0.9% = 0.009 (remember that you must divide by 100 to convert from a percentage to a decimal), and n = 42 (the year 2050 minus the year 2008). Plugging these into the formula, we find:P(1 + r)n = 301,000,000(1 + 0.009)42 = 301,000,000(1.009)42 = 301,000,000(1.457) = 438,557,000Therefore, the U.S. population is predicted to be 435,557,000 in the year 2050. Let’s consider the situation where we want to find out when the population will double. Let’s use this same example, but this time we want to find out when the doubling in population will occur assuming the same annual growth rate. We’ll set up the problem like the following:Double P = P(1 + r)n P will be 301 million, Double P will be 602 million, r = 0.009, and we will be looking for n. Double P = P(1 + r)n 602,000,000 = 301,000,000(1 + 0.009)nNow, we will divide both sides by 301,000,000. This will give us the following:2 = (1.009)nTo solve for n, we need to invoke a special exponent property of logarithms. If we take the log of both sides of this equation, we can move exponent as shown below:log 2 = log (1.009)n log 2 = n log (1.009)Now, divide both sides of the equation by log (1.009) to get:n = log 2 / log (1.009)Using the logarithm function of a calculator, this becomes:n = log 2/log (1.009) = 77.4Therefore, the U.S. population should double from 301 million to 602 million in 77.4 years assuming annual growth rate of 0.9 %. Now it is your turn:Search the Internet and determine the most recent population of your home state. A good place to start is the U.S. Census Bureau (www.census.gov) which maintains all demographic information for the country. If possible, locate the annual growth rate for your state. If you can not locate this value, feel free to use the same value (0.9%) that we used in our example above. Determine the population of your state 10 years from now. Determine how long and in what year the population in your state may double assuming a steady annual growth rate. Look up the population of the city in which you live. If possible, find the annual percentage growth rate of your home city (use 0.9% if you can not locate this value). Determine the population of your city in 10 years. Determine how long until the population of your city doubles assuming a steady growth rate. Discuss factors that could possibly influence the growth rate of your city and state. Do you live in a city or state that is experiencing growth? Is it possible that you live in a city or state where the population is on the decline or hasn’t changed? How would you solve this problem if the case involved a steady decline in the population (say -0.9% annually)? Show an example. Think of other real world applications (besides monitoring and modeling populations) where exponential equations can be utilized.

Fair Shares

Fair Shares

Fair SharesThe Center City Anuraphilic (frog lovers) society has fallen on hard times. Abraham, Bobby and Charlene are the only remaining members and each feels equally entitled to take possession of the society’s collection of live rare tropical frogs. The decision is made to use the method of sealed bids and fair shares to decide who will take possession of the entire collection and how much will be paid in compensation to the other members. Abraham unseals his estimate of the value of the collection at $12,000.00. Bobby’s estimate of the value of the collection is $6,000.00. Charlene values the collection at $9,000.00. Who receives the collection of frogs? What is each person’s fair share of the monetary value of the collection? Why is the monetary amount of each fair share different? How much money is owed to each of the two people who do not “win” the collection of frogs? In your opinion how “Fair” is the process described above? Now pretending for a moment that you like frogs, we will insert you into the situation under special circumstances. Despite (or perhaps because of) your love of all things amphibious, you currently lack the funds to pay each of the others their probable fair share. You will not receive the collection, but wish to receive as much money as possible. You have no knowledge of the amounts in each of the sealed bids, but strongly suspect that Abraham will bid between $10,000.00 and $12,000.00. Given that you cannot afford to “win” the process, describe how you will go about deciding what to put down for your own estimate of the value of the collection.

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