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 $ (17,773.17, 6.750.00, 11,570.00, or 12.773.17) and the amount of interest earned on the account is $ (17,773.17, 6.750.00, 11,570.00, or 12.773.17)
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 $ (17,773.17, 6.750.00, 11,570.00, or 12.773.17) and the amount of interest earned on the account is $ (17,773.17, 6.750.00, 11,570.00, or 12.773.17)
Answers
GPT-4o mini
To find the total value of the account 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:
\[ A = P(1 + r)^t \]
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).
- \( t \) is the time the money is invested for in years.
Given:
- \( P = 5000 \)
- \( r = 0.073 \) (7.3%)
- \( t = 18 \)
Substituting the values into the formula:
\[
A = 5000(1 + 0.073)^{18}
\]
Calculating this step by step:
\[
A = 5000(1.073)^{18}
\]
First, calculate \( (1.073)^{18} \):
\[
(1.073)^{18} \approx 3.6461
\]
Now, substituting back into the equation:
\[
A \approx 5000 \times 3.6461 \approx 18230.50
\]
So, the total value of the account after 18 years is approximately \( A \approx 18230.50 \).
Next, we can calculate the interest earned by subtracting the principal from the total amount:
\[
\text{Interest} = A - P = 18230.50 - 5000 \approx 13230.50
\]
Therefore, rounding to two decimal places:
The final amount of the college fund is **$18,230.50** and the amount of interest earned on the account is **$13,230.50**.
Since these values do not match the provided options, please double-check the options given in case of a discrepancy.
\[ A = P(1 + r)^t \]
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).
- \( t \) is the time the money is invested for in years.
Given:
- \( P = 5000 \)
- \( r = 0.073 \) (7.3%)
- \( t = 18 \)
Substituting the values into the formula:
\[
A = 5000(1 + 0.073)^{18}
\]
Calculating this step by step:
\[
A = 5000(1.073)^{18}
\]
First, calculate \( (1.073)^{18} \):
\[
(1.073)^{18} \approx 3.6461
\]
Now, substituting back into the equation:
\[
A \approx 5000 \times 3.6461 \approx 18230.50
\]
So, the total value of the account after 18 years is approximately \( A \approx 18230.50 \).
Next, we can calculate the interest earned by subtracting the principal from the total amount:
\[
\text{Interest} = A - P = 18230.50 - 5000 \approx 13230.50
\]
Therefore, rounding to two decimal places:
The final amount of the college fund is **$18,230.50** and the amount of interest earned on the account is **$13,230.50**.
Since these values do not match the provided options, please double-check the options given in case of a discrepancy.