Mathematics of Individual Finance

PROBLEMS

1. Paul buys a 5 year bank certificate of deposit (CD) which pays an annual rate of interest of 6%. If he puts $4,925 in the CD, how much will he have when it matures? [See Example 5-1]

2. Cindy deposits $3,890 in a bank account paying 4% per year, compounded and credited monthly. How much will she have at the end of 2 years? [See Example 5-2]

3. Bonnie puts $22,740 into a brokerage money market account that pays an annual rate of interest of 3.25% compounded and credited daily. How much would she have at the end of 120 days? [See Example 5-3]

4. In Problem 3, above, the money market states an annual percent rate of 3.25% per year. What is its effective annual rate as the result of daily compounding? [See Example 5-4]

5. Paulo wants to have $25,000 in his bank account to buy a four wheel drive vehicle for his son's 21st birthday which is three years away. He can invest his money in a 3 year CD which pays an annually compounded rate of 7%. How much must he put into the CD now to achieve his goal? [See Example 5-5]

6. Under the terms of his aunt's will, Charlie will receive $125,000 on his 30th birthday, which is 6 years away. Since the funds are kept for him by the trust department of a bank, Charlie has decided to use the 6 year CD bank rate of 6.35% for his discount rate. What is the present value of Charlie's inheritance? [See Example 5-6]

7. Ben has signed a no-cut major league contract which pays him 2.3 million dollars per year for five years. Using a discount rate of 7.5%, what is the present value of his contract? [See Example 5-7]

8. Billy-Joe has just retired and will receive an annuity of $1,857 per month for 25 years. Payments are made at the end of each month. If he uses an discount rate with an annual return of 6%, what is the present value of his annuity? [ See Example 5-8]

9. Polly just won the giant $25 million lottery. Today the Governor will give her the first of 20 annual checks for $1,250,000. The state bonds have a lousy credit rating and Polly wants to use a 9% discount rate to calculate the present value of her prize. What is it? [See Example 5-9]

10. Suzy will retire in 15 years at age 65. How much must she put aside as a lump sum now to insure monthly payments at retirement of $2,500 for 20 years using an annual rate of 8.5%? [See Example 5-10]

11. Phil wants to buy a 35 foot sailboat in about 5 years. If he manages to save $500 per month and makes the payments at the end of each month how much will he have accumulated at the end of 5 years if he manages to earn an annual rate of 9% on his savings? [See Example 5-11]

12. In Problem 11, Phil decides to make his first $500 deposit to his boat account immediately. Now, how much will he have at the end of the 5 years? [See Example 5-12]

13. Sara and June are in the market for a house. They found one for $210,000. They can get a 30 year mortgage at 8.2% and plan to make a downpayment of 20% of the selling price. What will be their monthly mortgage payment? [See Example 5-13]

14. In Problem 13, when Sara and June go to the bank, the are offered an annual percent rate of 7.75% if they take a 15 year loan rather than one for 30 years. What would be their mortgage payments under this plan? [See Example 5-14]

15. Linda is 23 year old MBA student who wants to be a millionaire by the time she is 40. She will graduate next year, on her 24th birthday, and expects to get a job paying $40,000 per year. If she can earn 12% on her money, what proportion of her expected annual gross salary must she save each year to realize her dream? [See Example 5-15]

16. Suppose Linda can only put aside $15,000 per year. How high a rate of return must she realize to achieve her goal? [See Example 5-16]

17. Keith owns a Treasury bond which pays a semi-annual coupon of $65. The bond will mature in 8 years and will repay the principal of $1,000 at maturity. If the yield curve shows that 8 year Treasuries have yields of 7.2% at the current time, how much is Keith's bond worth? [See Example 5-17]

18. Willy has just taken early retirement at age 52. He will receive $2,000 per month in retirement benefits until he turns 62 and begins receiving Social Security, at which time the pension declines to only $1,800 per month for 18 years. What is the present value of his pension if he uses an annual discount rate of 8%? [See Example 5-18]

19. Josh takes out a two year auto loan for $15,000 which calls for monthly payments at an annual rate of 11%. Calculate his monthly payment, his monthly interest payments and his balance at the end of each month. [See Example 5-19]

20. Jerry spends $25 per week having his lawn cut during the spring, summer and early fall months for a total of 20 weeks per year. He can purchase a riding lawn mower for $1,800 and expects that it will last for 8 years. Ignoring his costs for gasoline and repairs as well as the time he saves now and inflation, what is the net present value of the investment if we use a discount rate of 6%? [See Example 5-20]

21. Wendy is a 38 year old CPA earning $55,000 per year. She is thinking of taking an MBA degree which would enable her to $62,000 in today's dollars. The MBA requires 2 years of full time work and costs $20,000 per year. Using an inflation rate of 4% and a discount rate of 7%, is the MBA financially worthwhile if she plans to work to age 60? [See Example 5-21]

22. Jerry just obtained a fixed rate 10 year mortgage at 10%. What is the duration of his mortgage and what is the approximate maturity of a Treasury bond of equivalent duration? [See Example 5-23]