Answer:
$35,734.12
Explanation:
To determine the amount Joe must deposit now to have $75,000 in 18 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A is the future value we want to have ($75,000 in this case)
P is the present value we need to deposit now
r is the annual interest rate (3.75%)
n is the number of times interest is compounded per year (12 for monthly compounding)
t is the number of years (18)
Substituting the given values, we get:
$75,000 = P(1 + 0.0375/12)^(12*18)
Simplifying the exponent:
$75,000 = P(1.003125)^216
Dividing both sides by (1.003125)^216:
P = $75,000 / (1.003125)^216
P ≈ $35,734.12
Therefore, Joe must deposit approximately $35,734.12 now to have $75,000 in 18 years at an interest rate of 3.75% compounded monthly.