Final answer:
The value of Salvatore's mutual fund after 6 1/2 years if the fund earns 9% compounded annually is approximately $544.64.
Step-by-step explanation:
To calculate the value of the mutual fund after 6 1/2 years, we need to determine the future value of regular contributions made at the beginning of each quarter. The formula to calculate the future value is:
FV = P * ((1 + r/n)^(n*t) - 1) / (r/n)
Where FV is the future value, P is the regular payment, r is the interest rate, n is the number of times Compounded per year, and t is the number of years.
In this case, the regular payment is $640, the interest rate is 9% (0.09), the number of times Compounded per year is 1 (since it's compounded annually), and the number of years is 6 1/2 (6.5).
Substituting the values into the formula, we get:
FV = 640 * ((1 + 0.09/1)^(1*6.5) - 1) / (0.09/1)
FV = 640 * (1.75892318147325 - 1) / 0.09
FV = 640 * 0.75892318147325 / 0.09
FV = 544.64
Therefore, the value of Salvatore's mutual fund after 6 1/2 years will be approximately $544.64.