Question

Felix has $100 in an account that earns 5% interest compounded annually.

To the nearest cent, how much interest will he earn in 2 years?

Answer 1

[AI-generated answer — Bot GPT 3.5]

To calculate the interest earned in 2 years, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (the initial deposit or loan amount)
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per year
t = the number of years the money is invested or the loan is repaid

In this case, P = $100, r = 0.05 (5% expressed as a decimal), n = 1 (compounded annually), and t = 2 years.

Plugging these values into the formula, we get:

A = 100(1 + 0.05/1)^(1*2)
A = 100(1.05)^2
A = 100(1.1025)
A ≈ $110.25

To find the interest earned, we subtract the original principal from the future value:

Interest = A - P
Interest = $110.25 - $100
Interest ≈ $10.25

Therefore, Felix will earn approximately $10.25 in interest in 2 years.