Question

Starting on the day he retires, Bob wants to receive payments of 2000 at the beginning of each month for 20 years. How much money should he deposit each quarter starting today if he plans to retire in 35 years and he makes his last deposit three months before his retirement date? Assume that the account earns a nominal rate of 7% per year compounded quarterly for the first 35 years and then a nominal rate of 5%per year compounded monthly thereafter.

Answer 1

PVAnnuity Due = c*((1-(1+ i)^(-n))/i)*(1 + i )

C = Cash flow per period

i = interest rate

n = number of payments

PV= 2000*((1-(1+ 5/1200)^(-20*12))/(5/1200))*(1+5/1200)

PV = 304313.34

FVAnnuity Due = c*(((1+ i)^n - 1)/i)*(1 + i )

C = Cash flow per period

i = interest rate

n = number of payments

304313.34= Cash Flow*(((1+ 7/400)^(35*4)-1)/(7/400))*(1+7/400)

Cash Flow = 505.92