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# Time Value of Money

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Juan Garza invested \$20,000 10 years ago at 12 percent, compounded quarterly. How much has he accumulated?

What is the future value of a 10-year annuity of \$4,000 per period where payments come at the beginning of each period? The interest rate is 12 percent.

You need \$28,974 at the end of 10 years, and your only investment outlet is an 8 percent long-term certificate of deposit (compounded annually). With the certificate of deposit, you make an initial investment at the beginning of the first year.
a. What single payment could be made at the beginning of the first year to achieve this objective?
b. What amount could you pay at the end of each year annually for 10 years to achieve this same objective?

On January 1, 2002, Mike Irwin, Jr., bought 100 shares of stock at \$14 per share. On December 31, 2004, he sold the stock for \$21 per share. What is his annual rate of return? Interpolate to find the exact answer.

Bridget Jones has a contract in which she will receive the following payments for the next five years: \$1,000, \$2,000, \$3,000, \$4,000, and \$5,000. She will then receive an annuity of \$8,500 a year from the end of the 6th through the end of the 15th year. The appropriate discount rate is 14 percent. If she is offered \$30,000 to cancel the contract, should she do it?

#### Solution Preview

Juan Garza invested \$20,000 10 years ago at 12 percent, compounded quarterly. How much has he accumulated?

We need to find the Future Value (FV). Since it is quarterly compounding, the rate would be 12/4=3% and the number of periods would be 10X4=40.
Using the FIVF table, since it was a lump sum
FV = PV x FVIF (3%, 40 periods)
FV = \$20,000 x 3.262 = \$65,240

What is the future value of a 10-year annuity of \$4,000 per period where payments come at the beginning of each period? The interest rate is 12 percent.

This is a annuity due problem, since the payments come at the beginning of the peiod. In such a problem, we increase the time period by 1 and get the factor from the FVIFA table. In the factor we reduce by 1.
Here we use 11 periods and 12%. the factor is 20.655. This is reduced by 1=19.555.
FVA = A x FVIFA
n = 11, i = 12% . The factor is 20.655-1 = 19.655
FVA = \$4,000 x 19.655 = \$78,620

You need \$28,974 at the end of 10 years, and your only investment outlet is an 8 percent long-term certificate of deposit (compounded annually). With the certificate of deposit, you make an initial investment at the ...

#### Solution Summary

The solution has time value of money problems relating to present value and future value of annuities and single sum

\$2.19