Suppose that Ian Greitzer deposits his $13,000 bonus in an account that earns an annual rate of 8.5%, compounded quarterly, and makes additional deposits of $400 at the end of each quarter for the next 21.5 years, until he retires. How much was deposited? Round your answer to the nearest cent.
A)$458,674.18
B)$22,243.99
C)$175,312.58
D)$85,960,962.98
E)$19,932.99

Question

Suppose that Ian Greitzer deposits his $13,000 bonus in an account that earns an annual rate of 8.5%, compounded quarterly, and makes additional deposits of $400 at the end of each quarter for the next 21.5 years, until he retires. How much was deposited? Round your answer to the nearest cent. ​
A)$458,674.18
B)$22,243.99
C)$175,312.58
D)$85,960,962.98
E)$19,932.99

Quizplus · Accepted Answer

Using the formula for the future value of an annuity, we can calculate the total amount of deposits made by Ian:

PMT x [((1+r/n)^(n*t)-1)/(r/n)]

where PMT is the quarterly deposit ($400), r is the annual interest rate (8.5%), n is the number of times the interest is compounded per year (4), and t is the total number of periods (21.5 years x 4 quarters per year = 86 quarters).

Plugging in the values, we get:

$400 x [((1+0.085/4)^(4*86)-1)/(0.085/4)] = $175,312.58

Therefore, Ian deposited a total of $175,312.58 over the course of 21.5 years.

Suppose That Ian Greitzer Deposits His $13,000 Bonus in an Account