Question

Mitchell puts $100.00 into an account to use for school expenses. The account earns 9% interest, compounded annually. How much will be in the account after 10 years?
Round your answer to the nearest cent.

Answer 1

To determine how much will be in the account after 10 years with an initial deposit of $100.00, an annual interest rate of 9%, and compounded annually, we can use the formula for compound interest:

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

Where:
- \( A \) is the amount in the account after \( n \) years,
- \( P \) is the principal amount (the initial deposit),
- \( r \) is the annual interest rate (in decimal form),
- \( n \) is the number of years the money is invested or borrowed.

Given:
- \( P = 100.00 \) (initial deposit),
- \( r = 0.09 \) (9% as a decimal),
- \( n = 10 \) (the number of years).

Now, we can plug in the values:

\[
A = 100.00(1 + 0.09)^{10}
\]

Calculating the expression inside the parentheses:

\[
1 + 0.09 = 1.09
\]

Now we raise 1.09 to the power of 10:

\[
A = 100.00(1.09)^{10}
\]

Calculating \( (1.09)^{10} \):

\[
(1.09)^{10} \approx 2.36736
\]

Now multiplying by the principal:

\[
A \approx 100.00 \times 2.36736 \approx 236.736
\]

Rounding to the nearest cent, we get:

\[
A \approx 236.74
\]

Therefore, the amount in the account after 10 years will be **$236.74**.