This Discussion will help us learn to develop our own mathematical models, write down the equations and then solve the equations for unknown values using algebraic methods. Refer back to Week One Discussion and use the names and ages of yourself and the other two people you selected. Make sure one is older than you and one is younger than you. In years, how old was the older person when you were born? Write an equation that models how old in years each of you will be, when your ages add up to 150 years old. For example, if x = your age and the eldest person was a year older than you, you would write their age as x + 1. Then the equation would be: x + (x+1) = 150. Explain the reasoning which helped you develop your equation. Solve for your future ages. Are your answers reasonable, do they add up to 150? In years, how old were you when the youngest person was born? At some point during the lives of you and the youngest person, your age will be three times his/her age at that moment. Write an equation which models how old in years each of you will be when you are three times as old as the younger person. Explain the reasoning which helped you develop your equation. Solve the equation for your ages when you are three times as old as the youngest person. Are your answers reasonable? Respond to at least two of your classmates’ postings. Check their equations and investigate for mathematical errors. Help with a constructive critique. Your initial post should be at least 150 words in length.

Find the simple interest on a $400 investment made for 5 years at an interest rate of 7%/year. What is the accumulated amount? A) The simple interest is $140, the accumulated amount is $540. B) The simple interest is $115, the accumulated amount is $515. C) The simple interest is $120, the accumulated amount is $520. D) The simple interest is $125, the accumulated amount is $555. 2. If the accumulated amount is $3,720 at the end of 3 years and the simple rate of interest is 8%/year, what is the principal? A) The principal is $3,500. B) The principal is $3,360. C) The principal is $3,000. D) The principal is $3,200. 3. Find the accumulated amount A if the principal P = $2,000 is invested at the interest rate of r = 6% per year for t = 6 years, compounded annually. A) The accumulated amount is $3,508.28. B) The accumulated amount is $3,194.16. C) The accumulated amount is $2,837.04. D) The accumulated amount is $2,708.89. 4. Find the accumulated amount A if the principal P = $11,000 is invested at the interest rate of r = 5% per year for t = 5.5 years, compounded quarterly. A) The accumulated amount is $14,585.32. B) The accumulated amount is $13,785.93. C) The accumulated amount is $14,100.05. D) The accumulated amount is $14,457.17. 5. Determine the simple interest rate at which $1,500 will grow to $1,550 in the 8 months. Round your answers to the nearest tenth of percent. A) The interest rate is 5%/year. B) The interest rate is 4.33%/year. C) The interest rate is 4.76%/year. D) The interest rate is 66.67%/year. E) The interest rate is 3.06%/year. 6. Find the present value of $40,000 due in 4 years at the given rate of interest 8%/year compounded monthly. A) The present value is $28,948.67. B) The present value is $29,433.94. C) The present value is $29,076.82. D) The present value is $29,748.06. 7. In order to help finance the purchase of a new house, the Abdullahs have decided to apply for a short-term loan (a bridge loan) in the amount of $140,000 for a term of 1 mo. If the bank charges simple interest at the rate of 12%/year, how much will the Abdullahs owe the bank at the end of the term? A) $141,400 B) $140,012 C) $146,800 D) $144,900 8. The Kwans are planning to buy a house 6 years from now. Housing experts in their area have estimated that the cost of a home will increase at a rate of 6%/year during that period. If this economic prediction holds true, how much can the Kwans expect to pay for a house that currently costs $160,000? A) $218,199 B) $221,562 C) $230,490 D) $226,963 9. The manager of a money market fund has invested $4.2 million in certificates of deposit that pay interest at the rate of 5.4%/year compounded quarterly over a period of 5 years. How much will the investment be worth at the end of 5 years? A) 5,491,921.88 B) 3,211,990.34 C) 1,291,921.88 D) 12,024,347.20 10. Find the effective rate corresponding to nominal rate 6% / year compounded monthly. Round the answers to the nearest hundredth of percent. A) 6.538% B) 5.858% C) 6.598% D) 6.168% 11. Find the interest rate needed for an investment of $4,000 to grow to an amount of $5,000 in 4 yr if interest is compounded continuously. Please round the answer to the nearest hundredth of percent. A) 5.58 %/yr B) 5.70 %/yr C) 6.63 %/yr D) 5.01 %/yr E) 5.92 %/yr 12. Anthony invested a sum of money 6 yr ago in a savings account that has since paid interest at the rate of 7%/year compounded quarterly. His investment is now worth $19,713.77. How much did he originally invest? Please round the answer to the nearest cent. A) $13,000.01 B) $12,500.01 C) $14,000.01 D) $11,500.01 E) $11,000.01 13. Georgia purchased a house in 1998 for $220,000. In 2003 she sold the house and made a net profit of $50,000. Find the effective annual rate of return on her investment over the 5-yr period. Please round the answer to the nearest tenth of percent. A) 3.7%/yr B) 3.1%/yr C) 4.4%/yr D) 4.2%/yr E) 5.6%/yr 14. Find the amount of an ordinary annuity of 10 yearly payments of $1,800 that earn interest at 10% per year, compounded annually. A) $4,668.74 B) $28,687.36 C) $87,798.04 D) $3,600.00 15. Robin, who is self-employed, contributes $4,000/year into a Keogh account. How much will he have in the account after 15 years if the account earns interest at the rate of 6.5%/year compounded yearly? A) $96,728.68 B) $10,287.36 C) $158,267.14 D) $3,771.28 16. If a merchant deposits $1,500 annually at the end of each tax year in an IRA account paying interest at the rate of 10%/year compounded annually, how much will she have in her account at the end of 25 years? Round your answer to two decimal places. A) $16,252.06 B) $147,520.59 C) $5,250.00 D) $34,663.65 17. Find the present value of an ordinary annuity of $600 payments each made quarterly over 5 years and earning interest at 4% per year compounded quarterly. A) $8,154.20 B) $2,671.09 C) $10,827.33 D) $56,916.87 18. Juan invested $24,000 in a mutual fund 5 years ago. Today his investment is worth $34,616. Find the effective annual rate of return on his investment over the 5-year period. A) 10.3%/year B) 8%/year C) 83%/year D) 8.3%/year 19. Find the amount of an ordinary annuity for 5 years of quarterly payments of $2,200 that earn interest at 4% per year compounded quarterly. A) $11,222.21 B) $65,511.77 C) $48,441.81 D) $2,684.42 20. Find the present value of the ordinary annuity. Please round the answer to the nearest cent.$2,000 per semiannual period for 7 yr at 12%/year compounded semiannually A) P = $18,589.97 B) P = $17,913.54 C) P = $20,003.52 D) P = $13,147.80 E) P = $9,629.07

must show all work please and has to be correct. 1.  Marcia Stubern is planning for her golden years. She will retire in 20 years  at which time she plans to withdraw $60,000 annually. She is expected to live for 20 years following her retirement. Her financial advisor thinks she can earn 9% annually. How much does she need to invest each year to prepare for her financial needs after her retirement?2.  Samauel Johnson invested in gold 1 ounce "double eagle" U.S. coins ten years ago, paying $185 at that time. He could sell these coins for $734 today. What rate of return did he earn on this investment?3.  The Swell Computer Company has developed a new line of desktop computers. It is estimated that the cash return generated by the new product line will be $800,000 / year for the first 5 years and then $500,000 / year for 3 year after that. The cash returns occur at the end of each year. Using a discount rate of 9%, what is the present value of these returns?4.Ten years ago Harold black bought 100 shares of common stock of Country Homes for $37.50 per share. He just sold them  (ten years later) for a total of $9,715.02 Assume there were not any dividend payments during this 10 years. What was Harold's rate of return.5. Mr. Sullivan is borrowing  $2 million to expand his business. The loan will be for 10 years at 12% and will be repaid in equal quarterly installments. What will the amount of the quarterly payments be?I must show my work on each problem, Thank you for you help!!!