Suppose you invest every quarter, for 20 years, in an annuity that pays 5% interest, compounded quarterly. At the end of the 20 years, you have $100,000. How much of this total is interest

$41,228

Explanation:

The first step is to determine the amount that was being invested, in other words, the annuity.

First find the future value of annuity factor:

= 1 * Future value of annuity formula

= 1 * ( ( 1 + rate)^ number of periods) - 1) / rate

Rate = 5% / 4 = 1.25%

Number of periods = 20 * 4 quarters = 80 quarters

Annuity factor = 1 * ( ( 1 + 1.25%) ⁸⁰ - 1) / 1.25%

= 136.118795

The annuity is:

Future value of annuity = Annuity * Future value of annuity factor, 80 years, 1.25%

100,000 = Annuity * 136.118795

Annuity = 100,000 / 136.118795

= $734.65

The interest is:

= Future value of annuity - (Annuity * number of periods)

= 100,000 - (734.65 * 80)

= $41,228

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