# End of Chapter Questions

Show all work for the following questions

**(4-1) Future Value of a Single Payment**

If you deposit $10,000 in a bank account that pays 10% interest annually, how much will be in your account after 5 years?

**(4-2) Present Value of a Single Payment**

What is the present value of a security that will pay $5,000 in 20 years if securities of equal risk pay 7% annually?

**(4-3) Interest Rate on a Single Payment**

Your parents will retire in 18 years. They currently have $250,000, and they think they will need $1 million at retirement. What annual interest rate must they earn to reach their goal, assuming they don’t save any additional funds?

**(4-4) Number of Periods of a Single Payment**

If you deposit money today in an account that pays 6.5% annual interest, how long will it take to double your money?

**(4-5) Number of Periods for an Annuity**

You have $42,180.53 in a brokerage account, and you plan to deposit an additional $5,000 at the end of every future year until your account totals $250,000. You expect to earn 12% annually on the account. How many years will it take to reach your goal?

**(4-6) Future Value: Ordinary Annuity versus Annuity Due**

What is the future value of a 7%, 5-year ordinary annuity that pays $300 each year? If this were an annuity due, what would its future value be?

**(4-7) Present and Future Value of an Uneven Cash Flow Stream**

An investment will pay $100 at the end of each of the next 3 years, $200 at the end of Year 4, $300 at the end of Year 5, and $500 at the end of Year 6. If other investments of equal risk earn 8% annually, what is this investment’s present value? Its future value?

**(4-8) Annuity Payment and EAR**

You want to buy a car, and a local bank will lend you $20,000. The loan would be fully amortized over 5 years (60 months), and the nominal interest rate would be 12%, with interest paid monthly. What is the monthly loan payment? What is the loan’s EFF%?

**(4-9) Present and Future Values of Single Cash Flows for Different Periods**

Find the following values, using the equations, and then work the problems using a financial calculator to check your answers. Disregard rounding differences. (Hint: If you are using a financial calculator, you can enter the known values and then press the appropriate key to find the unknown variable. Then, without clearing the TVM register, you can “override” the variable that changes by simply entering a new value for it and then pressing the key for the unknown variable to obtain the second answer. This procedure can be used in parts b and d, and in many other situations, to see how changes in input variables affect the output variable.)

a. An initial $500 compounded for 1 year at 6%

b. An initial $500 compounded for 2 years at 6%

c. The present value of $500 due in 1 year at a discount rate of 6%

d. The present value of $500 due in 2 years at a discount rate of 6%

**(4-10) Present and Future Values of Single Cash Flows for Different Interest Rates**

Use both the TVM equations and a financial calculator to find the following values. See the Hint for Problem 4-9.

a. An initial $500 compounded for 10 years at 6%

b. An initial $500 compounded for 10 years at 12%

c. The present value of $500 due in 10 years at a 6% discount rate

d. The present value of $500 due in 10 years at a 12% discount rate

**(4-11) Time for a Lump Sum to Double**

To the closest year, how long will it take $200 to double if it is deposited and earns the following rates? [Notes: (1) See the Hint for Problem 4-9. (2) This problem cannot be solved exactly with some financial calculators. For example, if you enter PV = −200, PMT = 0, FV = 400, and I = 7 in an HP-12C and then press the N key, you will get 11 years for part a. The correct answer is 10.2448 years, which rounds to 10, but the calculator rounds up. However, the HP10BII gives the exact answer.]

a. 7%

b. 10%

c. 18%

d. 100%