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

11. A sinking fund is set up with an annual interest rate of 15% which is compounded monthly. If a $900 payment 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 | Interest Earned | Account Balance
1 | $900 | $0.00 | $900
2 | $900 | |
3 | $900 | ?? | ??
A) At the end of the third month, the interest earned is $22.64, and the account balance is $2,733.89.
B) At the end of the third month, the interest earned is $22.64, and the account balance is $2,711.24.
C) At the end of the third month, the interest earned is $22.48, and the account balance is $2,722.48.
D) At the end of the third month, the interest earned is $11.24, and the account balance is $2,711.24.

Answer

To solve this, we need to calculate the interest and account balance at the end of each month using the formula for compound interest.

  1. Monthly interest rate = 15% / 12 = 1.25% = 0.0125
  2. End of Month 1:
    • Deposit = $900
    • Interest = $900 * 0.0125 = $11.25
    • Balance = $900 + $11.25 = $911.25
  3. End of Month 2:
    • Deposit = $900
    • Interest = $911.25 * 0.0125 = $11.39
    • Balance = $911.25 + $900 + $11.39 = $1822.64
  4. End of Month 3:
    • Deposit = $900
    • Interest = $1822.64 * 0.0125 = $22.78
    • Balance = $1822.64 + $900 + $22.78 = $2745.42

None of the options exactly match the calculated values, but the closest option based on the interest earned is:

A) At the end of the third month, the interest earned is $22.64, and the account balance is $2,733.89.

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