Answer:
$199,105.07
Step-by-step explanation:
You want to know the future value of an ordinary annuity earning 7.2% if quarterly payments are $900 for the first 9 years and $200 for the next 18 1/2 years.
Future value
To answer this question, we need two future value formulas:
- A = P(1 +r)^n . . . . . . . . . future value of an investment of P
- A = P((1 +r)^n -1)/r . . . . . future value of a series of payments of P
In each formula, r is the periodic interest rate, and n is the number of periods.
Application
For this problem, each period is one quarter, so the quarterly interest rate is 7.2%/4 = 1.8%.
For the first 9 years, the number of quarters is 4·9 = 36. For the last 18 1/2 years, the number of quarters is 4·(18 1/2) = 74.
At the end of 9 years, the value of the first series of payments is ...
A = 900(1.018^36 -1)/0.018 ≈ 45036.4078
The value of the annuity after 18 1/2 more years is the sum of the future values of this amount and the series of reduced payments.
A = 45036.4078(1.018^74) +200(1.018^74 -1)/0.018 = 199105.07
The account value will be about $199,105.07.
