Question

Simon has $9,594 in an account. The interest rate is 5% compounded annually.
To the nearest cent, how much will he have in 2 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 balance in Simon's account after 2 years, we can 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.

Let's plug in the values:
- \( p = 9594 \)
- \( r = 5\% = 0.05 \)
- \( t = 2 \)

Now, substituting the values into the formula:

\[
B = 9594(1 + 0.05)^2
\]

Calculating \( (1 + 0.05)^2 \):

\[
1 + 0.05 = 1.05
\]
\[
1.05^2 = 1.1025
\]

Now substitute back into the equation:

\[
B = 9594 \times 1.1025
\]

Calculating the final amount:

\[
B = 10520.895
\]

Rounding to the nearest cent, Simon will have:

\[
\text{Final amount} = \$10,520.90
\]

Thus, after 2 years, Simon will have **$10,520.90** in his account.