## Time Value of Money

Self-Paced Overview

### Annuities

#### Using Tables to Solve Future Value of Annuity Problems

An annuity is an equal, annual series of cash flows. Annuities may be equal annual deposits, equal annual withdrawals, equal annual payments, or equal annual receipts. The key is *equal, annual* cash flows.

When cash flows occur at the end of the year, this makes them an ordinary annuity*Ordinary Annuity:*End of year cash flows.. If the cash flows were at the beginning of the year, they would be an annuity due*Annuity Due:*Beginning of year cash flows.. Annuities due will be covered a later.

Annuities work as follows:

- Annuity = Equal Annual Series of Cash Flows.
- Assume annual deposits of $100 deposited at end of year earning 5% interest for three years.

Year 1: $100 deposited at end of year

Year 2: $100 × .05 = $5.00 + $100 + $100

Year 3: $205 × .05 = $10.25 + $205 + $100

= $100.00

= $205.00

= $315.25

Again, there are tables for working with annuities. TVM Table 2: Future Value of Annuity Factors is the table to be used in calculating annuities due. Basically, this table works the same way as the previous table. Look up the appropriate number of periods, locate the appropriate interest, take the factor found and multiply it by the amount of the annuity.

For instance, on the three-year, 5% interest annuity of $100 per year. Going down three years, out to 5%, the factor of 3.152 is found. Multiply that by the annuity of $100 yields a future value of $315.20.

Another example of calculating the future value of an annuity is illustrated.

You deposit $300 each year for 15 years at 6%. How much will you have at the end of that time?

The Answer: Show Me