Acme Annuities recently offered an annuity that pays 4.5% compounded monthly. What equal monthly deposit should be made into this annuity in order to have 64000 in 18 years?
To find the equal monthly deposit required to have $64000 in 18 years with a 4.5% annual interest rate compounded monthly, we can use the formula for the future value of an ordinary annuity:
FV = P * ((1 + r)^n - 1) / r,
where:
FV = future value of the annuity ($64000),
P = monthly deposit,
r = monthly interest rate (4.5% / 12 = 0.045 / 12),
n = number of periods (18 years * 12 months/year = 216 months).
Substituting the given values into the formula, we get:
64000 = P * ((1 + (0.045 / 12))^216 - 1) / (0.045 / 12).
Simplifying further, we have:
64000 = P * (1.00375^216 - 1) / 0.00375.
Now, solving for P:
P = 64000 * 0.00375 / (1.00375^216 - 1).
Calculating this expression, we find that the equal monthly deposit required is approximately $205.40.