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# Present and Future Value Problems

1. If you invest \$100 at an interest rate of 15 percent, how much will you have at the end of 8 years?

2. An investment of \$232 will produce \$312.18 in 2 years. What is the annual interest rate?

3. You invest \$1,000 today and expect to sell your investment for \$2,000 in 10 years.
a. Is this a good deal if the discount rate is 5 percent?
b. What if the discount rate is 10 percent?

4. Investments in the stock market have increased at an average compound rate of about 10 percent since 1926.
a. If you invested \$1,000 in the stock market in 1926, how much would that investment be worth today?
b. If your investment in 1926 has grown to \$1 million, how much did you invest in 1926?

5. A famous quarterback just signed a \$15 million contract providing \$3 million a year for 5 years. A less famous receiver signed a \$14 million 5-year contract providing \$4 million now and \$2 million a year for 5 years. Who is better paid? The interest rate is 12 percent.

#### Solution Preview

1. If you invest \$100 at an interest rate of 15 percent, how much will you have at the end of 8 years?

Here you can use the FV table or you can use the formula for calculating the FV of an amount, the formula is:

FVamount =

=

2. An investment of \$232 will produce \$312.18 in 2 years. What is the annual interest rate?

Here we apply the same formula:

\$312.18 = \$232(1+r)2

1.3456 = (1+r)2

1.16 = 1 + r

r = 1.16 - 1

r = 0.16 = 16%

3. You invest \$1,000 today and expect to sell your investment for \$2,000 in 10 years.
a. Is this a good deal if the discount rate is 5 percent?

FVamount =

FV = \$1000 × 1.628.89

FV = ...

#### Solution Summary

This solution includes some Finance problems relating to Present and Future Value calculations. Solution includes step by step formulae. The solution answers the following problems step by step:
If you invest \$100 at an interest rate of 15 percent, how much will you have at the end of 8 years
An investment of \$232 will produce \$312.18 in 2 years. What is the annual interest rate?
You invest \$1,000 today and expect to sell your investment for \$2,000 in 10 years
Investments in the stock market have increased at an average compound rate of about 10 percent since 1926
A famous quarterback just signed a \$15 million contract providing \$3 million a year for 5 years. A less famous receiver signed a \$14 million 5-year contract providing \$4 million now and \$2 million a year for 5 years. Who is better paid?

\$2.19