To determine the monthly deposit needed to save $700,000 over 12 years with 9.75% interest compounded monthly, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment ($700,000 in this case)
P = the principal amount (the monthly deposit we're trying to find)
r = the annual interest rate (9.75% or 0.0975 as a decimal)
n = the number of times the interest is compounded per year (12 for monthly compounding)
t = the number of years (12 years in this case)
We need to rearrange the formula to solve for P:
P = A / (1 + r/n)^(nt)
Substituting the given values into the formula:
P = $700,000 / (1 + 0.0975/12)^(12*12)
P = $700,000 / (1.008125)^(144)
P ≈ $1,965.15
Therefore, the monthly deposit that should be made is approximately $1,965.15.
The correct answer is B. $1,965.15.