To find the total value of the college fund after 18 years with an initial investment of $5,000, an annual compound interest rate of 7.5%, 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:
- \( P = 5000 \)
- \( r = 7.5% = 0.075 \)
- \( n = 18 \)
Now, substituting the values into the formula:
\[ A = 5000(1 + 0.075)^{18} \]
Calculating \( (1 + 0.075) \):
\[ 1 + 0.075 = 1.075 \]
Next, calculate \( (1.075)^{18} \):
\[ (1.075)^{18} \approx 3.703 \]
Now, substitute this value back into the equation:
\[ A = 5000 \times 3.703 \approx 18515.00 \]
Now we can calculate the interest earned:
\[ \text{Interest Earned} = A - P = 18515.00 - 5000 = 13515.00 \]
So, the total value of the college fund is approximately $18,515.00, and the interest earned is approximately $13,515.00.
The final answers are:
- The final amount of the college fund is $(18515.00)$ and the amount of interest earned on the account is $(13515.00)$.