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 famed lightbulb importer, bought an annuity that pays $2,711.00 at the end of each year, for the next 3 years. The prevailing interest rate is 6%.

You've been briefed with the following facts:

  • The present value factor for an annuity due at 6% for 3 years is 2.83339.
  • The present value factor for an ordinary annuity at 6% for 3 years is 2.67301.
What is the present value of the annuity?

Answer:

  • $7,246.54

Explanation:

  1. Because the payments occur at the end of each period, the annuity is clearly an ordinary annuity (PV factor: 2.67301).
  2. Here's the formula to use
    PRESENT VALUE OF ANNUITY = PAYMENT * PRESENT VALUE FACTOR
  3. Let's just plug in the numbers
    $7,246.54 = $2,711.00 * 2.67301
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