Alan Jackson invests $20,000 at 8% annual interest, leaving the money invested without withdrawing any of the interest for 8 years. At the end of the 8 years, Alan withdraws the accumulated amount of money. a) Compute the amount Alan would withdraw assuming the investment earns simple interest. b) Compute the amount Alan would withdraw assuming the investment earns interest compounded annually. c) Compute the amount Alan would withdraw assuming the investment earns interest compounded semiannually.

a. $32,800

b. $37,019

c. $37,460

Explanation:

a. The computation of Total Amount Withdrawn by Alan when simple interest is shown below:-

Accumulated amount of money = Invested amount + (Rate of interest × Number of years)

= $20,000 + ($20,000 × 8% × 8)

= $32,800

b. The computation of Total Amount Withdrawn by Alan when annually Compounded is shown below:-

Accumulated amount of money = Invested amount × (1 + rate of interest)^Number of years

= $20,000 × (1 + 0.08)^8

= $20,000 × 1.85093

= $37,019

c. The computation of Total Amount Withdrawn by Alan when semi annually Compounded is shown below:-

Accumulated amount of money = Invested amount × (1 + rate of interest × Number of years ÷ 200)^16)

= ($20,000 × (1 + 0.08 × 8 ÷ 200)^16)

= $20,000 × 1.87298

= $37,460

Therefore we have applied the above formulas.

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