1. (7 points) If the real rate of interest is 6% and the nominal rate of interest is 8%, calculate the rate of inflation.

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1 1. (7 points) If the real rate of interest is 6% and the nominal rate of interest is 8%, calculate the rate of inflation. 2. (9 points) Sarah is the beneficiary of a Trust Fund. Each year for 10 years, she will receive a payment of 100,000. Sarah takes each payment and invests it in a fund earning an annual effective interest rate of 6%. How much will Sarah have one year after she receives her last payment from the trust fund.

2 3. (11 points) Sam wants to provide a perpetuity immediate with annual payments to the Purdue Actuarial Program. The first payment from the perpetuity will be $1000 payable in one year. Each year thereafter each payment will be 8% higher than the prior year payment. In other words, the second payment will be 1000(1.08), the third payment will be 1000(1.08) 2, etc. Calculate the present value of this perpetuity immediate using an annual effective interest rate of 10%. 4. (9 points) Liz invests 1000 today at 6% simple interest for 8 years. Nick invests X today at a nominal rate of interest of 8% compounded quarterly for the next 8 years. At the end of 8 years, Liz and Nick have the same amount of money. Calculate X.

3 5. (12 points) The force of interest δ t = 0.001t 2. Megan invests 1000 at t=4. Calculate the amount that she will have at t=8. 6. (12 points) Logan won the lottery. He has the option of receiving: a. an increasing perpetuity due where the annual payments start at 100 and increase by 100 each year; or b. A 10 year uniformly decreasing annuity immediate where the payments begin at 10P and decrease uniformly to P for the 10 th payment. At an annual effective rate of interest of 10%, the two options have an equal present value. Calculate P.

4 7. (8 points) A project has the following cash flows: Time Amount 0-1,000, , , , , ,000,000 Calculate the net present value of the cash flows at an interest rate equivalent to δ = (12 points) An annual annuity immediate pays 1000 at the end of the first year. Each subsequent payment increases by 200. In other words, the first payment is 1000, the second payment is 1200, the third payment is 1400, etc. The annuity continues for 12 years. Calculate the present value of this annuity at an annual effective rate of 8%.

5 Use the following information about an investment fund for problems 9 11: Time Fund Value Before Contributions Contributions 0 10,000 0 ¼ 8,000-3,000 ½ 8,000 3,000 ¾ 12,000 3, , (9 points) Calculate the exact annual dollar weighted return for the fund. 10. (9 points) Estimate the annual dollar weighted return for the fund assuming simple interest and all cash flows occurred in the middle of the year. 11. (9 points) Calculate the annual time weighted yield for this fund.

6 12. (10 points) An annuity makes monthly payments at the end of each month for 10 years. During the first 4 years, the monthly payment is 100. During the last 6 years, the monthly payment is 200. Calculate the current value of this annuity at the end of the fourth year assuming an interest rate of i (12) = (8 points) On January 1, 2007, Ki-cho makes a payment of 1000 to Irene. On that same date, Ki-cho pays Kuan a total of Two years later on January 1, 2009, Kuan makes a payment of 2500 to Irene. On January 1, 2012, Irene makes a payment of 4500 to Ki-cho. Calculate Ki-cho annual yield on this transaction.

7 14. (9 points) Alex wants to buy a house. To do so, he will take out a 30 year mortgage loan of $120,000 which he will repay with monthly payments. The interest rate on the mortgage loan is 8% compounded monthly. Calculate the amount of Alex monthly mortgage payment. 15. (11 points) If Alex pays 1000 per month (instead of the required payment that you calculated) on the mortgage that he took out in Question 12, what is his outstanding loan balance at the end of 10 years, right after the 120 th payment?

8 16. (11 points) An annuity pays 1 at the start of the first month. Each subsequent payment increases by 1 until a payment of 360 is paid at the start of the 360 th month. Calculate the accumulated value of this annuity at monthly effective interest rate of 1%. 17. (7 points) Matt invests 1000 at the end of each year for 10 years. At the end of 10 years, he has accumulated 12,500. Calculate the annual effective rate of interest earned by Matt.

9 18. (9 points) You are given the following table: Year 1 Year2 Year 3 Year 4 Year 5 Portfolio Year If a fund credits interest using the investment year method, how much will 1000 invested on January 1, 2000 accumulate to on December 31, 2006? 19. (8 points) Y is the exact number of years that it takes for money to double at 5% interest. Z is the estimated number of years that it will take for money to double using the Rule of 72. Y and Z are not necessarily integer. Calculate Y Z.