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 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 amount of money).
- \( r \) is the annual interest rate (decimal).
- \( n \) is the number of years the money is invested or borrowed.
Given:
- \( P = 5000 \)
- \( r = 0.073 \) (7.3% as a decimal)
- \( n = 18 \)
Now, plug in the numbers:
\[
A = 5000(1 + 0.073)^{18}
\]
Calculating \( 1 + 0.073 \):
\[
1 + 0.073 = 1.073
\]
Now raise \( 1.073 \) to the power of 18:
\[
1.073^{18} \approx 3.677187
\]
Now multiply by the principal:
\[
A = 5000 \times 3.677187 \approx 18385.935
\]
Rounding to two decimal places, the total amount in the account after 18 years is:
\[
A \approx 18385.94
\]
Next, to find the interest earned, we subtract the principal from the total amount:
\[
\text{Interest} = A - P = 18385.94 - 5000 = 13385.94
\]
Therefore, the final amount of the college fund and the interest earned are:
- The final amount of the college fund is **$18,385.94**.
- The amount of interest earned on the account is **$13,385.94**.
So the answers are:
- The final amount of the college fund is $**18,385.94**, and the amount of interest earned on the account is $**13,385.94**.
\[
A = P(1 + r)^n
\]
Where:
- \( A \) is the amount of money accumulated after n years, including interest.
- \( P \) is the principal amount (the initial amount of money).
- \( r \) is the annual interest rate (decimal).
- \( n \) is the number of years the money is invested or borrowed.
Given:
- \( P = 5000 \)
- \( r = 0.073 \) (7.3% as a decimal)
- \( n = 18 \)
Now, plug in the numbers:
\[
A = 5000(1 + 0.073)^{18}
\]
Calculating \( 1 + 0.073 \):
\[
1 + 0.073 = 1.073
\]
Now raise \( 1.073 \) to the power of 18:
\[
1.073^{18} \approx 3.677187
\]
Now multiply by the principal:
\[
A = 5000 \times 3.677187 \approx 18385.935
\]
Rounding to two decimal places, the total amount in the account after 18 years is:
\[
A \approx 18385.94
\]
Next, to find the interest earned, we subtract the principal from the total amount:
\[
\text{Interest} = A - P = 18385.94 - 5000 = 13385.94
\]
Therefore, the final amount of the college fund and the interest earned are:
- The final amount of the college fund is **$18,385.94**.
- The amount of interest earned on the account is **$13,385.94**.
So the answers are:
- The final amount of the college fund is $**18,385.94**, and the amount of interest earned on the account is $**13,385.94**.