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 $ _______
First options are ; 17,773.17
6.750.00
11,570.00
12.773.17
Second options are : 17,773.17
6.750.00
11,570.00
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 $ ________
and the amount of interest earned on the
account is $ _______
First options are ; 17,773.17
6.750.00
11,570.00
12.773.17
Second options are : 17,773.17
6.750.00
11,570.00
12.773.17
Answers
GPT-4o mini
To calculate the total value of Martin's college fund after 18 years with 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:
- \( P = 5000 \)
- \( r = 0.073 \)
- \( n = 18 \)
Now, plug the values into the formula:
\[
A = 5000(1 + 0.073)^{18}
\]
\[
A = 5000(1.073)^{18}
\]
Calculating \((1.073)^{18}\):
\[
(1.073)^{18} \approx 3.554069
\]
Now multiply by the principal:
\[
A \approx 5000 \times 3.554069 \approx 17770.345
\]
Rounding to two decimal places, we get:
\[
A \approx 17770.35
\]
Next, we'll calculate the interest earned:
\[
\text{Interest} = A - P = 17770.35 - 5000 = 12770.35
\]
Rounding to two decimal places, we find:
- Total value of the account after 18 years: **$17,770.35**
- Amount of interest earned on the account: **$12,770.35**
Since your options are slightly different, we'll match the closest values with the appropriate context from your options.
### Final Values
The total value of the college fund is **$17,773.17** (rounded to the nearest provided option).
The amount of interest earned on the account is **$12,773.17** (rounded to the nearest provided option).
Thus:
The final amount of the college fund is **$17,773.17**
and the amount of interest earned on the account is **$12,773.17**.
\[
A = P(1 + r)^n
\]
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:
- \( P = 5000 \)
- \( r = 0.073 \)
- \( n = 18 \)
Now, plug the values into the formula:
\[
A = 5000(1 + 0.073)^{18}
\]
\[
A = 5000(1.073)^{18}
\]
Calculating \((1.073)^{18}\):
\[
(1.073)^{18} \approx 3.554069
\]
Now multiply by the principal:
\[
A \approx 5000 \times 3.554069 \approx 17770.345
\]
Rounding to two decimal places, we get:
\[
A \approx 17770.35
\]
Next, we'll calculate the interest earned:
\[
\text{Interest} = A - P = 17770.35 - 5000 = 12770.35
\]
Rounding to two decimal places, we find:
- Total value of the account after 18 years: **$17,770.35**
- Amount of interest earned on the account: **$12,770.35**
Since your options are slightly different, we'll match the closest values with the appropriate context from your options.
### Final Values
The total value of the college fund is **$17,773.17** (rounded to the nearest provided option).
The amount of interest earned on the account is **$12,773.17** (rounded to the nearest provided option).
Thus:
The final amount of the college fund is **$17,773.17**
and the amount of interest earned on the account is **$12,773.17**.