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.
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.
Answers
GPT-4o mini
To calculate the total value of the 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.
In this case:
- \( P = 5000 \)
- \( r = 0.073 \)
- \( n = 18 \)
Now we can substitute these values into the formula:
\[
A = 5000 \times (1 + 0.073)^{18}
\]
Calculating \( 1 + 0.073 \):
\[
1 + 0.073 = 1.073
\]
Now we raise this to the power of 18:
\[
1.073^{18} \approx 3.478
\]
Now we multiply by the principal amount:
\[
A \approx 5000 \times 3.478 \approx 17390.09
\]
So, the total amount in the account after 18 years is approximately **$17,390.09**.
Next, to find the interest earned, we subtract the principal from the total amount:
\[
\text{Interest} = A - P = 17390.09 - 5000 = 12390.09
\]
Thus, the interest earned on the account is approximately **$12,390.09**.
In conclusion:
- Total value of the account after 18 years: **$17,390.09**
- Interest earned on the account: **$12,390.09**
\[
A = P(1 + r)^n
\]
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.
In this case:
- \( P = 5000 \)
- \( r = 0.073 \)
- \( n = 18 \)
Now we can substitute these values into the formula:
\[
A = 5000 \times (1 + 0.073)^{18}
\]
Calculating \( 1 + 0.073 \):
\[
1 + 0.073 = 1.073
\]
Now we raise this to the power of 18:
\[
1.073^{18} \approx 3.478
\]
Now we multiply by the principal amount:
\[
A \approx 5000 \times 3.478 \approx 17390.09
\]
So, the total amount in the account after 18 years is approximately **$17,390.09**.
Next, to find the interest earned, we subtract the principal from the total amount:
\[
\text{Interest} = A - P = 17390.09 - 5000 = 12390.09
\]
Thus, the interest earned on the account is approximately **$12,390.09**.
In conclusion:
- Total value of the account after 18 years: **$17,390.09**
- Interest earned on the account: **$12,390.09**