Question

Spencer deposited $10 in an account earning 5% interest compounded annually. To the nearest cent, how much will he have in 3 years?

Answer 1

To calculate the amount in the account after 3 years with an initial deposit of $10 and an interest rate of 5% compounded annually, we can use the formula for compound interest:

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

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

Given:
- \( P = 10 \)
- \( r = 0.05 \) (5% as a decimal)
- \( t = 3 \)

Now plug the values into the formula:

\[
A = 10 (1 + 0.05)^3
\]
\[
A = 10 (1.05)^3
\]
\[
A = 10 (1.157625)
\]
\[
A = 11.57625
\]

Rounding to the nearest cent, Spencer will have approximately:

\[
\boxed{11.58}
\]

So, after 3 years, Spencer will have $11.58 in the account.