Question

4. Calculate annuity cash flows Your goal is to have $20,000 in your bank account by the end of nine years. If the interest rate remains constant at 10% and you want to make annual identical deposits, you'll have to deposit into your account at the end of each year to reach your goal. If your deposits were made at the beginning of each year rather than an at the end, the amount of your deposit would change by _ still wanted to reach your financial goal by the end of nine years. if you Grade I NON

Answer 1

a). Annual Deposit = [FV required * r] / [(1 + r)ⁿ - 1]

= [$20,000 * 0.10] / [(1 + 0.10)⁹ - 1]

= $2,000 / 1.3579 = $1,472.81

b). FV of Annuity Due = FV of Ordinary Annuity * (1 + r) = $20,000 * (1 + 0.10) = $22,000

Annual Deposit = [FV required * r] / [(1 + r)ⁿ - 1]

= [$22,000 * 0.10] / [(1 + 0.10)⁹ - 1]

= $2,200 / 1.3579 = $1,620.09

Change in annual deposit = $1,620.09 - $1,472.81 = $147.28