Question

11. A sinking fund is set up with an annual interest rate of, 15% which is compounded monthly. If a $900 payme

is made at the end of each month, calculate both the interest earned and the account balance at the end of the
third month.
Period
Amount of Deposit
1
$900
2
$900
3
$900
At the end of the third month, the interest earned is $22.64, and the account balance is $2,733.89.
Interest Earned
$0.00
??
O At the end of the third month, the interest earned is $22.64, and the account balance is $2,711.24.
At the end of the third month, the interest earned is $11.24, and the account balance is $2,711.24
At the end of the third month, the interest earned is $22.48, and the account balance is $2, 722.48.
Account Balance
$900
??

Answer 1

(a) Interest: $22.64; Balance: $2733.89

Explanation:

You want a 3-month schedule of payments, interest, and the account balance for a sinking fund earning 15% APR on deposits of $900 made at the end of each month.

Interest

The interest earned by the account in any given month is the product of the monthly interest rate and the ending balance for the previous month.

The monthly interest rate is 15%/12 = 1.25%. For the second month, interest will be ...

$900 × 1.25% = $11.25

For the third month, interest will be ...

$1811.25 × 1.25% = $22.64

After the payment at the end of the third month, the account balance will be ...

$1811.25 +900.00 +22.64 = $2733.89

__

Additional comment

Total interest earned is $33.89 by the end of the third month. The answer choices seem to be telling you to interpret the question as asking for the interest earned in the third month, not the total interest earned.