Question
Derek deposited $7,000 in an account earning 15% 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 interest earned after 3 years, we can use the formula:
\[
B = p(1 + r)^t
\]
Where:
- \( B \) is the balance after time \( t \),
- \( p \) is the principal amount,
- \( r \) is the annual interest rate (as a decimal),
- \( t \) is the number of years.
Given values:
- \( p = 7000 \) (the principal)
- \( r = 15\% = 0.15 \) (the interest rate as a decimal)
- \( t = 3 \) (the time in years)
Now, we plug in the values:
\[
B = 7000(1 + 0.15)^3
\]
Calculating inside the parentheses first:
\[
B = 7000(1.15)^3
\]
Now, calculate \( (1.15)^3 \):
\[
(1.15)^3 = 1.15 \times 1.15 \times 1.15 = 1.520875
\]
Now, substitute this back into the equation for \( B \):
\[
B = 7000 \times 1.520875 = 10646.125
\]
Now we need to find the interest earned, which is the final balance \( B \) minus the principal \( p \):
\[
\text{Interest} = B - p = 10646.125 - 7000
\]
\[
\text{Interest} = 3646.125
\]
To round to the nearest cent, the interest earned in 3 years is:
\[
\text{Interest} \approx 3646.13
\]
So, Derek will earn approximately **$3,646.13** in interest over 3 years.
\[
B = p(1 + r)^t
\]
Where:
- \( B \) is the balance after time \( t \),
- \( p \) is the principal amount,
- \( r \) is the annual interest rate (as a decimal),
- \( t \) is the number of years.
Given values:
- \( p = 7000 \) (the principal)
- \( r = 15\% = 0.15 \) (the interest rate as a decimal)
- \( t = 3 \) (the time in years)
Now, we plug in the values:
\[
B = 7000(1 + 0.15)^3
\]
Calculating inside the parentheses first:
\[
B = 7000(1.15)^3
\]
Now, calculate \( (1.15)^3 \):
\[
(1.15)^3 = 1.15 \times 1.15 \times 1.15 = 1.520875
\]
Now, substitute this back into the equation for \( B \):
\[
B = 7000 \times 1.520875 = 10646.125
\]
Now we need to find the interest earned, which is the final balance \( B \) minus the principal \( p \):
\[
\text{Interest} = B - p = 10646.125 - 7000
\]
\[
\text{Interest} = 3646.125
\]
To round to the nearest cent, the interest earned in 3 years is:
\[
\text{Interest} \approx 3646.13
\]
So, Derek will earn approximately **$3,646.13** in interest over 3 years.