To calculate the total value of the college fund after 18 years with an initial amount 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:
- \( A \) = the amount of money accumulated after n years, including interest.
- \( P \) = the principal amount (the initial amount of money).
- \( r \) = annual interest rate (decimal).
- \( n \) = number of years the money is invested for.
Given:
- \( P = 5000 \)
- \( r = 7.3% = 0.073 \)
- \( n = 18 \)
Substituting in the values:
\[ A = 5000(1 + 0.073)^{18} \] \[ A = 5000(1.073)^{18} \]
Next, we calculate \( (1.073)^{18} \):
\[ (1.073)^{18} \approx 3.67932 \quad (\text{using a calculator}) \]
Now, substituting this back into the formula:
\[ A \approx 5000 \times 3.67932 \approx 18396.60 \]
Thus, the total amount in the college fund after 18 years is approximately \( A = 18396.60 \).
To find the interest earned on the account, we subtract the initial principal from the total amount:
\[ \text{Interest} = A - P \] \[ \text{Interest} = 18396.60 - 5000 = 13396.60 \]
Therefore, the final values rounded to two decimal places are:
- The final amount of the college fund is $18,396.60.
- The amount of interest earned on the account is $13,396.60.