Question

Samuel wants to deposit $5,000 and keep that money in the bank without deposits or withdrawals for 3 years. He compare two different options. Option 1 will pay 1.6% interest compounded quarterly. Option 2 will pay 1.5 % interest compounded continuously. Which option pays higher interest? How much higher? Responses

Answer 1

Option 1 earns approximately $25.93 more interest than Option 2 over 3 years.

Option 1 Calculation:

Future value (A1) with compound interest:

A1 = P * (1 + r/n)^(n*t)

A1 = 5000 * (1 + 0.016/4)^(4 * 3)

A1 = 5000 * (1.004)^12

A1 ≈ 5000 * 1.051675

A1 ≈ 5258.37

Option 2 Calculation:

Future value (A2) with continuous interest:

A2 = P * e^(rt)

A2 = 5000 * e^(0.015 * 3)

A2 ≈ 5000 * 1.046487

A2 ≈ 5232.44

Comparison:

Difference = A1 - A2

Difference ≈ 5258.37 - 5232.44

Difference ≈ 25.93