Answer: $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
