Question
Bernie deposited $2,000 in an account earning 10% interest compounded annually.
To the nearest cent, how much will he have in 5 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 he have in 5 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 5 years using the formula \( B = p(1 + r)^t \), we can plug in the given values:
- \( p = 2000 \) (the principal)
- \( r = 0.10 \) (the interest rate as a decimal)
- \( t = 5 \) (the time in years)
Now, substituting these values into the formula:
\[
B = 2000(1 + 0.10)^5
\]
Calculating inside the parentheses first:
\[
1 + 0.10 = 1.10
\]
Now raising \( 1.10 \) to the power of 5:
\[
1.10^5 \approx 1.61051
\]
Now, multiplying by the principal:
\[
B = 2000 \times 1.61051 \approx 3221.02
\]
Thus, to the nearest cent, Bernie will have approximately:
\[
\boxed{3221.02}
\]
- \( p = 2000 \) (the principal)
- \( r = 0.10 \) (the interest rate as a decimal)
- \( t = 5 \) (the time in years)
Now, substituting these values into the formula:
\[
B = 2000(1 + 0.10)^5
\]
Calculating inside the parentheses first:
\[
1 + 0.10 = 1.10
\]
Now raising \( 1.10 \) to the power of 5:
\[
1.10^5 \approx 1.61051
\]
Now, multiplying by the principal:
\[
B = 2000 \times 1.61051 \approx 3221.02
\]
Thus, to the nearest cent, Bernie will have approximately:
\[
\boxed{3221.02}
\]