Question

Account A and Account B both have a principal of $2,000 and an annual interest rate of 5%. No additional deposits or withdrawals are made. Account A earns simple interest. Account B earns interest compounded annually. Compare the amounts in the two accounts after 20 years. Which earns more interest? How much more?

Answer 1

Which earns more interest = Account B

How much more = $1,306.60

Explanation:

Given;

Principal P = $2,000

Interest rate r = 5% = 0.05

Time t = 20 years

For account A;

Simple interest = P×r×t

Substituting the values;

Simple interest = 2,000 × 0.05 × 20 = $2000

Interest on account A = $2,000

For account B;

Compound interest

Final amount = P(1 + r)^t

Since it's compounded annually

Substituting the values;

Final amount = 2000(1+0.05)^20

Final amount = $5306.60

Interest = final amount - principal = $5306.60 -$2000

Interest = $3,306.60

Therefore, account B earns more interest.

Difference = account B interest - account A interest

Difference = $3,306.60 - $2,000

Difference = $1,306.60