Question
When Martin was born, his father set up a $5,000 college fund for him with an annual compound interest rate of 7.3%.
What is the total value of this account after 18 years, and what was the interest earned on the account? Round the answers to two decimal places.
*Remember to use your STAAR Reference Sheet for support!
(2 points)
The final amount of the college fund is $
, and the amount of interest earned on the account is $ .
What is the total value of this account after 18 years, and what was the interest earned on the account? Round the answers to two decimal places.
*Remember to use your STAAR Reference Sheet for support!
(2 points)
The final amount of the college fund is $
, and the amount of interest earned on the account is $ .
Answers
GPT-4o mini
To calculate the total value of Martin's college fund after 18 years with an initial investment of $5,000 and an annual compound interest rate of 7.3%, we can use the formula for compound interest:
\[
A = P(1 + r)^n
\]
where:
- \(A\) is the total amount of money accumulated after n years, including interest.
- \(P\) is the principal amount (the initial investment).
- \(r\) is the annual interest rate (decimal).
- \(n\) is the number of years the money is invested.
Let's plug in the values:
- \(P = 5000\)
- \(r = 0.073\) (7.3% as a decimal)
- \(n = 18\)
Now we calculate \(A\):
\[
A = 5000(1 + 0.073)^{18}
\]
\[
A = 5000(1.073)^{18}
\]
Now we calculate \((1.073)^{18}\):
\[
(1.073)^{18} \approx 3.572658
\]
Now replace this back into the equation for \(A\):
\[
A = 5000 \times 3.572658 \approx 17863.29
\]
The total value of the college fund after 18 years is approximately \$17,863.29.
Next, we need to calculate the interest earned:
\[
\text{Interest} = A - P
\]
\[
\text{Interest} = 17863.29 - 5000 = 12863.29
\]
Thus, the final amounts are:
- The final amount of the college fund is **$17,863.29**.
- The amount of interest earned on the account is **$12,863.29**.
\[
A = P(1 + r)^n
\]
where:
- \(A\) is the total amount of money accumulated after n years, including interest.
- \(P\) is the principal amount (the initial investment).
- \(r\) is the annual interest rate (decimal).
- \(n\) is the number of years the money is invested.
Let's plug in the values:
- \(P = 5000\)
- \(r = 0.073\) (7.3% as a decimal)
- \(n = 18\)
Now we calculate \(A\):
\[
A = 5000(1 + 0.073)^{18}
\]
\[
A = 5000(1.073)^{18}
\]
Now we calculate \((1.073)^{18}\):
\[
(1.073)^{18} \approx 3.572658
\]
Now replace this back into the equation for \(A\):
\[
A = 5000 \times 3.572658 \approx 17863.29
\]
The total value of the college fund after 18 years is approximately \$17,863.29.
Next, we need to calculate the interest earned:
\[
\text{Interest} = A - P
\]
\[
\text{Interest} = 17863.29 - 5000 = 12863.29
\]
Thus, the final amounts are:
- The final amount of the college fund is **$17,863.29**.
- The amount of interest earned on the account is **$12,863.29**.