Question

You want to make equal deposits at the end of each month for 10 years into an account with annual interest rate 8% compounded monthly, and then withdraw $200 at the end of each month for the following 15 years, ending with a zero balance. How much do your monthly deposits need to be?

Answer 1

For second annuity, monthly withdrawal = $200 at the end of each month for 15 years

interest rate = 8% compounded monthly.

So, this is an ordinary annuity PV at the year 10 from now is

PV = PMT*(1 - (1+r/n)^(-n*t))/(r/n) = 200*(1 - (1 + 0.08/12)^(-12*15))/(0.08/12) = $20928.12

Now this value is final value for the 1st annuity for 10 years. So, here PMT is calculated using formula

PMT = FV*(r/n)/((1+r/n)^(n*t) - 1) = 20928.12*(0.08/12)/((1+0.08/12)^(12*10) -1) = $114.40

So, monthly deposits now should be $114.40