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.
(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.
(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 find the total value of the 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 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 or borrowed.
Given:
- \( P = 5000 \)
- \( r = 7.3\% = 0.073 \)
- \( n = 18 \)
Substituting these values into the formula:
\[
A = 5000(1 + 0.073)^{18}
\]
\[
A = 5000(1.073)^{18}
\]
Calculating \( (1.073)^{18} \):
\[
(1.073)^{18} \approx 3.575
\]
Now, calculating \( A \):
\[
A \approx 5000 \times 3.575 \approx 17875
\]
So, the total amount in the college fund after 18 years is approximately \( A \approx 17875.00 \).
To calculate the interest earned, we can subtract the principal from the total amount:
\[
\text{Interest} = A - P
\]
\[
\text{Interest} \approx 17875 - 5000 \approx 12875.00
\]
Thus, rounding to two decimal places:
- The final amount of the college fund is **$17,875.00**.
- The amount of interest earned on the account is **$12,875.00**.
Final answers:
- The final amount of the college fund is **$17,875.00**.
- The amount of interest earned on the account is **$12,875.00**.
\[
A = P(1 + r)^n
\]
where:
- \( A \) is the 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 or borrowed.
Given:
- \( P = 5000 \)
- \( r = 7.3\% = 0.073 \)
- \( n = 18 \)
Substituting these values into the formula:
\[
A = 5000(1 + 0.073)^{18}
\]
\[
A = 5000(1.073)^{18}
\]
Calculating \( (1.073)^{18} \):
\[
(1.073)^{18} \approx 3.575
\]
Now, calculating \( A \):
\[
A \approx 5000 \times 3.575 \approx 17875
\]
So, the total amount in the college fund after 18 years is approximately \( A \approx 17875.00 \).
To calculate the interest earned, we can subtract the principal from the total amount:
\[
\text{Interest} = A - P
\]
\[
\text{Interest} \approx 17875 - 5000 \approx 12875.00
\]
Thus, rounding to two decimal places:
- The final amount of the college fund is **$17,875.00**.
- The amount of interest earned on the account is **$12,875.00**.
Final answers:
- The final amount of the college fund is **$17,875.00**.
- The amount of interest earned on the account is **$12,875.00**.