Question
Sam has $50 in an account that earns 5% interest compounded annually.
To the nearest cent, how much interest will he earn 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.
To the nearest cent, how much interest will he earn 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.
Answers
GPT-4o mini
To calculate the amount of interest Sam will earn in 3 years, we can use the formula for compound interest:
\[
B = p(1 + r)^t
\]
where:
- \( B \) is the balance after \( t \) years,
- \( p \) is the principal (starting amount),
- \( r \) is the interest rate expressed as a decimal,
- \( t \) is the time in years.
Given:
- \( p = 50 \) (the starting amount),
- \( r = 0.05 \) (5% expressed as a decimal),
- \( t = 3 \) (time in years).
Now substitute these values into the formula:
\[
B = 50(1 + 0.05)^3
\]
Calculating the expression inside the parentheses:
\[
1 + 0.05 = 1.05
\]
Now we compute \( 1.05^3 \):
\[
1.05^3 \approx 1.157625
\]
Now calculate \( B \):
\[
B \approx 50 \times 1.157625 \approx 57.88125
\]
To find the interest earned, we subtract the principal from the balance:
\[
\text{Interest} = B - p = 57.88125 - 50 \approx 7.88125
\]
Rounding to the nearest cent, the interest Sam will earn in 3 years is:
\[
\text{Interest} \approx 7.88
\]
Thus, the amount of interest Sam will earn in 3 years is **$7.88**.
\[
B = p(1 + r)^t
\]
where:
- \( B \) is the balance after \( t \) years,
- \( p \) is the principal (starting amount),
- \( r \) is the interest rate expressed as a decimal,
- \( t \) is the time in years.
Given:
- \( p = 50 \) (the starting amount),
- \( r = 0.05 \) (5% expressed as a decimal),
- \( t = 3 \) (time in years).
Now substitute these values into the formula:
\[
B = 50(1 + 0.05)^3
\]
Calculating the expression inside the parentheses:
\[
1 + 0.05 = 1.05
\]
Now we compute \( 1.05^3 \):
\[
1.05^3 \approx 1.157625
\]
Now calculate \( B \):
\[
B \approx 50 \times 1.157625 \approx 57.88125
\]
To find the interest earned, we subtract the principal from the balance:
\[
\text{Interest} = B - p = 57.88125 - 50 \approx 7.88125
\]
Rounding to the nearest cent, the interest Sam will earn in 3 years is:
\[
\text{Interest} \approx 7.88
\]
Thus, the amount of interest Sam will earn in 3 years is **$7.88**.