Question

What is the value of an annuity that pays $685 at the end of each year in years 3 through 14 at the end of year 21? The discount rate (opportunity cost) is 3.7%. (That is, find the value of this annuity at the end of year 21). Round to the nearest $1, no $ symbol.
Blank 1. Calculate the answer by read surrounding text.

Answer 1

Given about an annuity that pays $685 at the end of each year in years 3 through 14

So, annual payment A = $685

time period t = 12 years

interest rate r = 3.7%

So, value of this ordinary annuity at year 14 using FV formula is

FV = A*((1+r)^t - 1)/r = 685*(1.037^12 - 1)/0.037 = $10117.32

Value of annuity at year 14 = $10117.32

its values at year 21 using compounding is

Value at 21 = value at 14*(1+r)^7 = 10117.32*1.037^7 = $13047.18

the value of this annuity at the end of year 21 = $13047.18