To calculate the future value of the investment with monthly compounding, we can use the formula:
A = P(1 + r/n)^(nt)
where:
A is the future value of the investment
P is the initial principal amount (in this case, $3,000)
r is the annual interest rate (7%)
n is the number of times the interest is compounded per year (12 for monthly compounding)
t is the number of years (10)
Using these values, we can calculate the future value of the investment with monthly compounding:
A = $3,000(1 + 0.07/12)^(12*10) = $6,802.64
Next, we can calculate the future value of the investment with annual compounding:
A = $3,000(1 + 0.07)^(10) = $6,727.50
The difference in future value between the two compounding methods is:
$6,802.64 - $6,727.50 = $75.14
Therefore, the future value of the investment would increase by $75.14 if the interest were compounded monthly instead of annually.