Question

Andre has an IRA, which compounds quarterly and pays 8% interest. Find the future value of his IRA if he

deposits $1,500 into his IRA at the beginning of each quarter for 5 years.

$36, 446.06
$38,674.98
$37, 174.98
$16,424.58

Answer 1

(c) $37,174.98

Explanation:

You want the future value of a quarterly payment of $1500 for 5 years into an account earning 8%, when payments are made at the beginning of the month.

Future value

You can use a suitable calculator (or spreadsheet) to find the future value of the series of payments. It will tell you the value is $37,174.98.

Alternatively, you can use the formula for the sum of a geometric sequence, with consideration given to the fact that the last payment earns a full quarter's interest.

FV = P(1 +r/n)((1 +r/n)^(nt) -1)/(r/n)

FV = 1500(1 +.08/4)((1.02^(4·5) -1)/(.02) ≈ 37174.976

The future value is $37,174.98.

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Additional comment

The functions provided by a calculator or spreadsheet allow for payments to be made that the beginning or the end of the period. You need to make sure to select "beginning". That is the default for the calculator shown in the attachment.