Question
Sofia has $7,306 in an account. The interest rate is 8% compounded annually.
To the nearest cent, how much will she 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.
$
To the nearest cent, how much will she 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.
$
Answers
GPT-4o mini
To calculate the balance after 2 years using the formula \( B = p(1 + r)^t \), we can plug in the values:
- \( p = 7306 \) (the initial amount)
- \( r = 0.08 \) (the interest rate of 8% expressed as a decimal)
- \( t = 2 \) (the number of years)
Now substituting these values into the formula:
\[
B = 7306(1 + 0.08)^2
\]
First, calculate \( (1 + 0.08) \):
\[
1 + 0.08 = 1.08
\]
Now square \( 1.08 \):
\[
(1.08)^2 = 1.1664
\]
Next, multiply this by the principal:
\[
B = 7306 \times 1.1664
\]
Calculating this product:
\[
B = 8533.0784
\]
Now round to the nearest cent:
\[
B \approx 8533.08
\]
Thus, the amount Sofia will have in 2 years is **$8,533.08**.
- \( p = 7306 \) (the initial amount)
- \( r = 0.08 \) (the interest rate of 8% expressed as a decimal)
- \( t = 2 \) (the number of years)
Now substituting these values into the formula:
\[
B = 7306(1 + 0.08)^2
\]
First, calculate \( (1 + 0.08) \):
\[
1 + 0.08 = 1.08
\]
Now square \( 1.08 \):
\[
(1.08)^2 = 1.1664
\]
Next, multiply this by the principal:
\[
B = 7306 \times 1.1664
\]
Calculating this product:
\[
B = 8533.0784
\]
Now round to the nearest cent:
\[
B \approx 8533.08
\]
Thus, the amount Sofia will have in 2 years is **$8,533.08**.