Question

Assume that a one-year CD purchased for $1000 pays an APR of 10% that is compounded semi-annually. How much is in the account at the end of each compounding period? (Calculate the interest and compound it each period rather than using the compound interest formula. Round your answers to the nearest cent.)

Answer 1

Answer:

• At the end of the first compounding period: $1,050.00

• At the end of the second compounding period: $1,102.50

Explanation:

1. First period:

• Investment: $1,000

• APR =  10% = 0.1 compounded semi-annually.

• Semi-annually compound interest: 0.1 / 2 = 0.05

• Interest earned at the end of the first period: $1,000 × 0.05 = $50.00

• Amount in the accoun at the end of the first period:

                                                        $1,000.00 + $50.00 = $1,050.00

2. Second period

• Amount in the account beginning the second period: $1,050.00

• Semi-annually compound interest: 0.1 / 2 = 0.05

• Interest earned in the second period:

                                                      $1,050.00  × 0.05 = $50.00 = $52.50

• Amount in the account at the end of the second period:

                                                     $1,050.00 + $52.50 = $1,102.50

Answer 2

The amount in the one-year CD account at the end of each compounding period is:

1st compounding period = $1,050.

2nd compounding period = $1,102.50

Data and Calculations:

Value of one-year CD = $1,000

APR = 10%

Interest for the 1st six months = $50 ($1,000 x 10% x 1/2)

Value of account at 1st compounding period = $1,050 ($1,000 + $50)

Interest for the 2nd six months = $52.50 ($1,050 x 10% x 1/2)

Value of account at 1st compounding period = $1,1,02.50 ($1,050 + $52.50)

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