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The amount of $2,800 is deposited into a sinking fund at the end of every semi-annual period for 5 years....

20. The amount of $2,800 is deposited into a sinking fund at the end of every semi-annual period for 5 years. Assume the interest rate is 7.5% compounded semi-annually.
What is the account balance after 1 year?
Period | Amount of Deposit | Interest Earned | Account Balance
1 | $2,800 | $0.00 | $2,800
2 | $2,800 | | ??
3 | $2,800 |
4 | $2,800 |
$2,905
$5,705
$105
$2,800

Answer

To find the account balance after 1 year, we need to calculate the interest earned and the total balance after two periods (since 1 year consists of two semi-annual periods).

  1. After the first period, the account balance is $2,800 with $0 interest earned.
  2. For the second period, the interest is calculated on the first deposit of $2,800. The interest rate per period is 7.5% / 2 = 3.75%.
  3. Interest earned after the second period = $2,800 * 0.0375 = $105.
  4. Total account balance after the second period = $2,800 (first deposit) + $2,800 (second deposit) + $105 (interest) = $5,705.

The account balance after 1 year is $5,705.

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