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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
Ginny LLC, the mysterious blanket manufacturer, bought an annuity that pays $3,402.00 at the start of each year, for the next 5 years. The prevailing interest rate is 10%.

This is what you've been told:

  • The present value factor for an annuity due at 10% for 5 years is 4.16987.
  • The present value factor for an ordinary annuity at 10% for 5 years is 3.79079.
What is the present value of the annuity?
Answer
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👉 Answer:

  • $14,185.88

👩‍🎓 This is how we solve it:

  1. Because the payments occur at the start of each period, the annuity is clearly an annuity due (PV factor: 4.16987).
  2. Here's the formula to use
    PRESENT VALUE OF ANNUITY = PAYMENT * PRESENT VALUE FACTOR
  3. Let's just plug in the numbers
    $14,185.88 = $3,402.00 * 4.16987
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