Question

Braden has $700 in an account that earns 10% interest compounded annually.
To the nearest cent, how much will he have in 3 years?
Use the formula B=p(1+r)t, where B is the balance (final amount), p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years

Answer 1

To calculate the amount Braden will have in 3 years, we can use the formula for compound interest, which is given as:

\[
B = p(1 + r)^t
\]

Where:
- \( B \) is the final amount (balance),
- \( p \) is the principal amount (initial amount),
- \( r \) is the annual interest rate (as a decimal),
- \( t \) is the time in years.

Given:
- \( p = 700 \) (the principal),
- \( r = 10\% = 0.10 \) (the interest rate as a decimal),
- \( t = 3 \) (the time in years).

We can now substitute these values into the formula:

\[
B = 700(1 + 0.10)^3
\]

Calculating \( 1 + 0.10 \):

\[
1 + 0.10 = 1.10
\]

Now we raise \( 1.10 \) to the power of \( 3 \):

\[
(1.10)^3 = 1.331
\]

Now, we multiply this result by the principal:

\[
B = 700 \times 1.331
\]

Calculating the final amount:

\[
B = 931.70
\]

Thus, to the nearest cent, Braden will have **$931.70** in his account after 3 years.