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The payments made in a sinking fund are $5,000 at the end of each quarter for 3 years. Assume the interest...

3. The payments made in a sinking fund are $5,000 at the end of each quarter for 3 years. Assume the interest rate is 10% compounded quarterly.
Calculate the interest earned at the end of Period 2.
Period | Amount of Deposit | Interest Earned | Account Balance
1 | $5,000 | $0.00 | $5,000
2 | $5,000 | ?? |
3 | $5,000 | |
4 | $5,000 | |
$125
$500
$12.50
$12,500

Answer

To calculate the interest earned at the end of Period 2, we use the formula for compound interest:

Interest = Principal × (1 + Rate)^n - Principal

Where:

  • Principal = $5,000 (the amount at the end of Period 1)
  • Rate = 10% per year compounded quarterly = 2.5% per quarter = 0.025
  • n = 1 (since we are calculating for one quarter)

Interest = $5,000 × (1 + 0.025)^1 - $5,000

Interest = $5,000 × 1.025 - $5,000

Interest = $5,125 - $5,000

Interest = $125

The interest earned at the end of Period 2 is $125.

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