Nikodemus s S. answered • 03/18/23
Determine the accumulated value of monthly deposits of $770 each after 10 years if the deposits earn 9.9%/year compounded quarterly. Assume that the deposits are made at the end of each month and that the compound interest is paid for part of an interest period (i,e. For any fractional interest compounding period)
To calculate the accumulated value of monthly deposits with quarterly compounding, we need to use the formula for the future value of an ordinary annuity with quarterly compounding:
FV = PMT * ((1 + r/q)^(n*q) - 1) / (r/q)
where:
PMT = the monthly payment or deposit ($770 in this case)
r = the annual interest rate (9.9%)
q = the number of compounding periods per year (4 for quarterly compounding)
n = the number of years (10 in this case)
Plugging in the values, we get:
FV = 770 * ((1 + 0.099/4)^(10*4) - 1) / (0.099/4)
FV ≈ $141,206.52
Therefore, the accumulated value of monthly deposits of $770 each after 10 years with quarterly compounding at an annual interest rate of 9.9% is approximately $141,206.52.
