To calculate the total value of the college fund after 18 years with an initial amount of $5,000 and a compound interest rate of 7.3%, we can use the compound interest formula:
\[ A = P(1 + r)^n \]
Where:
- \( A \) is the total amount after \( n \) years,
- \( P \) is the principal amount (initial investment),
- \( r \) is the annual interest rate (as a decimal),
- \( n \) is the number of years the money is invested or borrowed.
Given:
- \( P = 5000 \)
- \( r = 7.3% = 0.073 \)
- \( n = 18 \)
Substituting the values into the formula:
\[ A = 5000(1 + 0.073)^{18} \]
Calculating \( 1 + 0.073 \):
\[ 1 + 0.073 = 1.073 \]
Now calculating \( 1.073^{18} \):
\[ 1.073^{18} \approx 3.660583 \]
Now calculate \( A \):
\[ A \approx 5000 \times 3.660583 \approx 18302.915 \]
Rounding to two decimal places, the total amount in the account after 18 years is:
\[ A \approx 18302.92 \]
Next, we need to find the interest earned. The interest earned can be calculated as:
\[ \text{Interest} = A - P \]
Substituting the values:
\[ \text{Interest} = 18302.92 - 5000 = 13302.92 \]
Thus, rounding to two decimal places, the interest earned on the account is:
\[ \text{Interest} \approx 13302.92 \]
So, the final answers are:
- The total value of the college fund is $18,302.92.
- The amount of interest earned on the account is $13,302.92.