Annuities

Lesson:

Many business transactions involve a temporary stream of payments. Loans, for instance, are often paid over the course of many years at a set interest rate.

This stream of equal payments is often called an annuity.

There are two types of annuities:

  • Ordinary annuities are paid at the end of each period.
  • Annuities due are paid at the beginning of each period.

A simple trick to remember the difference is that the earlier in the name you see the word annuity, the sooner in a period each payment is required.

Inputting the type of annuity, the number of periods, and the interest rate into a complicated formula yields the present value factor. Multiplying this factor by the size of a single payment provides the present value of the stream of payments.

Charlie LLC, the ever-maligned tire exporter, bought an annuity that pays $7,620.00 at the end of each year, for the next 8 years. The prevailing interest rate is 3%.

The only relevant information you've discovered is as follows:

  • The present value factor for an ordinary annuity at 3% for 8 years is 7.01969.
  • The present value factor for an annuity due at 3% for 8 years is 7.23028.
What is the present value of the annuity?

Answer:

  • $53,490.05

Explanation:

  1. Because the payments occur at the end of each period, the annuity is clearly an ordinary annuity (PV factor: 7.01969).
  2. Here's the formula to use
    PRESENT VALUE OF ANNUITY = PAYMENT * PRESENT VALUE FACTOR
  3. Let's just plug in the numbers
    $53,490.05 = $7,620.00 * 7.01969
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