Question
Rob has $5,000 in an account that earns 2% 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.
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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 future balance in Rob's account using the formula \( B = p(1 + r)^t \), we need to identify the values for \( p \), \( r \), and \( t \):
- \( p = 5000 \) (the principal amount)
- \( r = 0.02 \) (the interest rate expressed as a decimal, which is 2% written as 0.02)
- \( t = 5 \) (the time in years)
Now we can plug these values into the formula:
\[
B = 5000(1 + 0.02)^5
\]
Calculating \( 1 + 0.02 \):
\[
1 + 0.02 = 1.02
\]
Next, raise \( 1.02 \) to the power of 5:
\[
1.02^5 \approx 1.1040808
\]
Now multiply this result by the principal amount:
\[
B = 5000 \times 1.1040808 \approx 5520.404
\]
Rounding this to the nearest cent, we get:
\[
B \approx 5520.40
\]
So, to the nearest cent, Rob will have **$5,520.40** in 5 years.
- \( p = 5000 \) (the principal amount)
- \( r = 0.02 \) (the interest rate expressed as a decimal, which is 2% written as 0.02)
- \( t = 5 \) (the time in years)
Now we can plug these values into the formula:
\[
B = 5000(1 + 0.02)^5
\]
Calculating \( 1 + 0.02 \):
\[
1 + 0.02 = 1.02
\]
Next, raise \( 1.02 \) to the power of 5:
\[
1.02^5 \approx 1.1040808
\]
Now multiply this result by the principal amount:
\[
B = 5000 \times 1.1040808 \approx 5520.404
\]
Rounding this to the nearest cent, we get:
\[
B \approx 5520.40
\]
So, to the nearest cent, Rob will have **$5,520.40** in 5 years.