1 - Purdue University



Math 373

Test 1

February 12, 2008

1. (6 points) Darren invests money in a bank account. During the year, his real rate of interest is 3% even though the rate of interest is on his account is 9%. Calculate the rate of inflation.

2. (10 points) Kevin invests 100 in a bank account earning a simple interest rate of 10%. James invests 100 in a bank account which earns an annual effective discount rate of d. At the end of 10 years, Kevin and James have the same amount of money in their accounts. Calculate d.

3. (12 points) Kurt is the beneficiary of a trust. Under the trust, he will receive payments at the end of each year for the next 20 years. The payment will be 2000 at the end of one year. Each subsequent payment will increase by 8%. In other words, the payment at the end of the second year will be 2000(1.08), the payment at the end of the third year will be 2000(1.082), etc. Calculate the present value of Kurt’s payments under the trust using an annual effective interest rate of 9%.

4. (8 points) Frank makes a loan to Ed. The amount of the loan is 4000. At the end of year 2, Ed makes a loan payment of 2500 to Frank. Frank reinvests the payment at an annual interest rate of 5%. At the end of year 4, Ed pays off the loan with another payment of 2500. Calculate Frank’s annual rate of return on the loan taking into account reinvestment.

5. (14 points) While Aiman is attending Purdue, he is receiving an annuity. The annuity pays monthly payments at the end of each month for four years. The payments start at 1000 in the first month and increase by 200 each month. In other words, the first payment is 1000, the second payment is 1200, the third payment is 1400, etc. Aiman takes each payment and invests the payments in a fund earning 8% compounded monthly. Calculate the amount that Aiman will have in the fund at the end of 4 years.

6. (6 points) Aaron has borrowed 20,000 to buy a new car. He will repay the loan with level monthly payments for 5 years. The interest rate on the loan is an annual effective rate of 6%. Calculate Aaron’s monthly payment.

7. (14 points) Sarah is receiving a perpetuity of 1000 payable at the beginning of each year. John is receiving a perpetuity immediate that pays 200 at the end of year one, 400 at the end of year two, 600 at the end of year three, etc. The present value of Sarah’s perpetuity is equal to the present value of John’s perpetuity if the present values are calculated at i. Calculate i.

8. (8 points) Hennessey Corporation is building a new factory. The factory is expected to generate the following cash flows:

|Time |Cash Flow |

|0 |-100 |

|1 |-10 |

|2 |40 |

|3 |60 |

|4 |80 |

Calculate the net present value of this project at 15%. Calculate the internal rate of return.

9. (8 points) Kyle has agreed to pay Aaron 1000 now. In two years, Aaron will pay Andrew a payment of 600. At the end of four years Aaron will pay Kyle a payment of 700. Also, at the end of four years, Andrew will make a payment of 800 to Kyle plus a payment of 100 to Aaron. Using the bottom line approach, what is Kyle’s annual return on this transaction?

10. (8 points) You are given that δt = 0.01t. John invests Z at time equal to zero. At time 5, he has 5000. Calculate Z.

11. (12 points) Angela has a loan which is to be repaid with annual payments at the end of each year for the next 20 years. The payments start at 2000 and decrease by 100 each year until 100 is paid at the end of year 20. In other words, the payments are 2000, 1900, 1800, etc. Angela is paying an annual effective interest rate of 12% on her loan. Calculate the original amount of Angela’s loan.

12. (12 points) Rob wants to accumulate 20,000 to buy a car at the end of 4 years. He is going to make four annual payments into a fund earning a nominal interest rate of 8% compounded quarterly. The level payments are being made at the beginning of each of the next four years. How much is each payment?

13. (12 points) Mark each the following true or false.

14. (12 points) Thomas bought a house 5 years ago. In order to buy the house, he borrowed 50,000 to be repaid with 360 monthly payments of 424.08. Thomas pays 424.08 each month for 60 months. Calculate outstanding loan balance on Thomas’ loan immediately after the 60th payment.

15. (8 points) Jennifer invests 1000 in a fund earning an annual effective interest rate of 10%. She wants to know when she will have 4000. Her banker estimates the time using the Rule of 72 as X years. Jennifer calculates it exactly as Y years. X and Y are not necessarily integers. Calculate Y - X.

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