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# Time Value of Money

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What is the present value of:
a. \$9,000 in 7 years at 8 percent?
b. \$20,000 in 5 years at 10 percent?
c. \$10,000 in 25 years at 6 percent?
d. \$1,000 in 50 years at 16 percent?

How much would you have to invest today to receive:
a. \$15,000 in 8 years at 10 percent?
b. \$20,000 in 12 years at 13 percent?
c. \$6,000 each year for 10 years at 9 percent?
d. \$50,000 each year for 50 years at 7 percent?

Your rich godfather has offered you a choice of one of the three following
alternatives: \$10,000 now; \$2,000 a year for eight years; or \$24,000 at the end
of eight years. Assuming you could earn 11 percent annually, which alternative
should you choose? If you could earn 12 percent annually, would you still
choose the same alternative?

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?

#### Solution Preview

What is the present value of:

All present value problems are to be handled using the PVIF table if the amount is a lump sum or the PBVIFA table if the amount is an annuity. The PV factor can be found by looking at the interest rate and the time period.

a. \$9,000 in 7 years at 8 percent?

Using the PVIF table, for 7 years and 8%, the factor is 0.583. The present value is 9000X0.583=5,247
b. \$20,000 in 5 years at 10 percent?
In the same way the facotor is 0.621 and PV is 12420
c. \$10,000 in 25 years at 6 percent?
Factor is 0.233 and PV is 2,330
d. \$1,000 in 50 years at 16 percent?
Factor is .001 and PV is 1

How much would you have to invest today to receive:
These are future value problems and can be solved using the PVIF table for a lumpsum and FVIFA table for an annuity. The FV factor can belooked up under the time period and interest ...

#### Solution Summary

The solution has various time value of money problems relating to calculation of present and future values

\$2.19