Question

Ashley puts $400.00 into an account to use for school expenses. The account earns 1% interest, compounded annually. How much will be in the account after 6 years?
Round your answer to the nearest cent.

Answer 1

To find the amount in the account after 6 years with compound interest, we can use the formula for compound interest:

\[
A = P(1 + r)^n
\]

where:
- \(A\) is the amount of money accumulated after n years, including interest.
- \(P\) is the principal amount (the initial amount of money).
- \(r\) is the annual interest rate (decimal).
- \(n\) is the number of years the money is invested or borrowed.

In this case:
- \(P = 400.00\)
- \(r = 0.01\) (1% expressed as a decimal)
- \(n = 6\)

Now we can plug in the values into the formula:

\[
A = 400(1 + 0.01)^6
\]

Calculating the expression inside the parentheses:

\[
A = 400(1.01)^6
\]

Now calculate \( (1.01)^6 \):

\[
(1.01)^6 \approx 1.061677812
\]

Now substituting this value back into the equation:

\[
A \approx 400 \times 1.061677812
\]

Calculating this gives:

\[
A \approx 424.671125
\]

Finally, rounding to the nearest cent:

\[
A \approx 424.67
\]

So, the amount in the account after 6 years will be approximately **$424.67**.