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Annuities

Lesson
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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.

Question
Juliet Corp., the acclaimed pillow manufacturer, bought an annuity that pays $8,994.00 at the start of each year, for the next 7 years. The prevailing interest rate is 7%.

You've been provided with the following information:

  • The present value factor for an ordinary annuity at 7% for 7 years is 5.38929.

  • The present value factor for an annuity due at 7% for 7 years is 5.76654.

What is the present value of the annuity?
Answer
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👉 Answer:

  • $51,864.26

👨‍🎓 Here's how we arrived at the answer:

  1. Because the payments occur at the start of each period, the annuity is clearly an annuity due (PV factor: 5.76654).
  2. Here's the formula to use
    PRESENT VALUE OF ANNUITY = PAYMENT * PRESENT VALUE FACTOR
  3. Let's just plug in the numbers
    $51,864.26 = $8,994.00 * 5.76654
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