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