Annie has $9,000 in an account that earns 5% interest compounded annually.

Question

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

Answer 1

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

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

Where:
- A is the final amount (including both principal and interest)
- P is the principal amount (the initial amount)
- r is the annual interest rate (expressed as a decimal)
- n is the number of times that interest is compounded per year
- t is the number of years

In this case, we have:
- P = $9,000
- r = 5% (or 0.05 as a decimal)
- n = 1 (compounded annually)
- t = 2 years

Substituting the values into the formula:

A = $9,000(1 + 0.05/1)^(1*2)
A = $9,000(1.05)^2
A ≈ $9,000(1.1025)
A ≈ $9,927.50

To find the interest earned, we subtract the initial principal from the final amount:

Interest Earned = $9,927.50 - $9,000 = $927.50

Therefore, Annie will earn approximately $927.50 in interest in 2 years.