Advanced Problems on Time Value of Money

1. What is the present value of $2,000 to be received two years from now, and another $3,000 to be received three years from now, at a rate of return of 7.6% per year?

2. The number of periods does not have to be measured in years. The periods can be anything: months, weeks, quarters, etc. Just make sure the rate is given for the same type of period. In other words, if t is measured in weeks, then the rate must be a rate per week. If t is measured in quarters, then the rate must be a rate per quarter. So what is the future value of $5,000 at the end of six months, if the rate of return is one-half percent per month?

3. The quarterly returns on my investment account over the past year have been as follows:

First Quarter5% Second Quarter 2% Third Quarter7% Fourth Quarter 1.5%

If I had $12,000 in the account at the beginning of the year, what is the value in the account at the end of the fourth quarter?

4. Suppose the value of a $1,000 investment went up 15% in its first year, and down 3% in its second year. What was the average rate of return over the two-year period?

5. Solving for the number of periods is easiest to do using the TVM keys on your calculator. For example, suppose an investor places $950 in an investment which earns interest at the rate of 12% per year. Later, the investment has grown to a value of $1,494.50. How many years did that take?