Question

Debra deposits $90,000 into an account that pays 3% interest per year, compounded annually. Dan deposits $90,000 into an account that also pays 3% per year. But it is simple interest. Find the interest Debra and Dan earn during each of the first three years. Then decide who earns more interest for each year. Assume there are no withdrawals and no additional deposits. Year First Second Third Interest Debra earns (Interest compounded annually) $0 $0 $ Interest Dan earns (Simple interest) $0 SA $ $ Who earns more interest? Debra earns more. Dan earns more. They earn the same amount. Debra earns more. Dan earns more. They earn the same amount. Debra earns more. Dan earns more. They earn the same amount.​

Answer 1

Explanation:

To solve this problem, we can use the formulas for simple interest and compound interest:

For simple interest:

Interest = Principal x Rate x Time

For compound interest:

Future Value = Principal x (1 + Rate)^Time

Interest = Future Value - Principal

where Principal is the initial amount invested, Rate is the annual interest rate, and Time is the duration of the investment.

For Debra:

Principal = $90,000

Rate = 3%

Time = 1 year

First year:

Interest = $90,000 x 0.03 x 1 = $2,700

Future Value = $90,000 x (1 + 0.03)^1 = $92,700

Interest = $92,700 - $90,000 = $2,700

Second year:

Interest = $92,700 x 0.03 x 1 = $2,781

Future Value = $90,000 x (1 + 0.03)^2 = $95,427

Interest = $95,427 - $90,000 = $5,427 - $2,700 = $2,727

Third year:

Interest = $95,427 x 0.03 x 1 = $2,863.81

Future Value = $90,000 x (1 + 0.03)^3 = $98,364.81

Interest = $98,364.81 - $90,000 = $8,364.81 - $5,427 = $2,937.81

For Dan:

Principal = $90,000

Rate = 3%

Time = 1 year

First year:

Interest = $90,000 x 0.03 x 1 = $2,700

Second year:

Interest = $90,000 x 0.03 x 1 = $2,700

Third year:

Interest = $90,000 x 0.03 x 1 = $2,700

Therefore, for each of the first three years, Debra earns more interest than Dan. In the first year, both earn the same amount of interest because the interest is calculated on the same principal amount. However, in the following years, Debra earns more interest because the interest is calculated on the principal plus the accumulated interest from the previous years.