**Week 2 Problem Set**

**Answer the following questions and solve the following problems in the space provided. When you are done, save the file in the format flastname_Week_2_Problem_Set.docx, where flastname is your first initial and you last name, and submit it to the appropriate dropbox.**

**Chapter 4 (pages 132–136):**

**3.** Calculate the future value of $2000 in

a. five years at an interest rate of 5% per year;

b. ten years at an interest rate of 5% per year; and

c. five years at an interest rate of 10% per year.

d. Why is the amount of interest earned in part (a) less than half the amount of interest earned in part (b)?

**4. **What is the present value of $10,000 received

a. twelve years from today when the interest rate is 4% per year;

b. twenty years from today when the interest rate is 8% per year; and

c. six years from today when the interest rate is 2% per year?

**5. **Your brother has offered to give you either $5,000 today or $10,000 in 10 years. If the interest rate is 7% per year, which option is preferable?

**6. **Consider the following alternatives.

i. $100 received in 1 year

ii. $200 received in 5 years

iii. $300 received in 10 years

a. Rank the alternatives from most valuable to least valuable if the interest rate is 10% per year.

b. What is your ranking if the interest rate is only 5% per year?

c. What is your ranking if the interest rate is 20% per year?

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**8. **Your daughter is currently 8 years old. You anticipate that she will be going to college in 10 years. You would like to have $100,000 in a savings account to fund her education at that time. If the account promises to pay a fixed interest rate of 3% per year, how much money do you need to put into the account today to ensure that you will have $100,000 in 10 years?

**9. **You are thinking of retiring. Your retirement plan will pay you either $250,000 immediately on retirement or $350,000 5 years after the date of your retirement. Which alternative should you choose if the interest rate is

a. 0% per year;

b. 8% per year; and

c. 20% per year?

**14. **You have been offered a unique investment opportunity. If you invest $10,000 today, you will receive $500 1 year from now, $1,500 2 years from now, and $10,000 10 years from now.

a. What is the NPV of the opportunity if the interest rate is 6% per year? Should you take the opportunity?

b. What is the NPV of the opportunity if the interest rate is 2% per year? Should you take it now?

**36. **You are thinking of purchasing a house. The house costs $350,000. You have $50,000 in cash that you can use as a down payment on the house, but you need to borrow the rest of the purchase price. The bank is offering a 30-year mortgage that requires annual payments and has an interest rate of 7% per year. What will your annual payment be if you sign up for this mortgage?

**37. **You would like to buy the house and take the mortgage described in Problem 36. You can afford to pay only $23,500 per year. The bank agrees to allow you to pay this amount each year, yet still borrow $300,000. At the end of the mortgage (in 30 years), you must make a *balloon* payment; that is, you must repay the remaining balance on the mortgage. How much will this balloon payment be?

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**38. **You have just made an offer on a new home and are seeking a mortgage. You need to borrow $600,000.

a. The bank offers a 30-year mortgage with fixed monthly payments and an interest rate of 0.5% per month. What is the amount of your monthly payment if you take this loan?

b. Alternatively, you can get a 15-year mortgage with fixed monthly payments and an interest rate of 0.4% per month. How much would your monthly payments be if you take this loan instead?

***A.1. This problem is from the Appendix to Chapter 4.**

Your grandmother bought an annuity from Rock Solid Life Insurance Company for $200,000 when she retired. In exchange for the $200,000, Rock Solid will pay her $25,000 per year until she dies. The interest rate is 5%. How long must she live after the day she retired to come out ahead (that is, to get more in *value* than what she paid in)?

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