Question

You wish to retire in 40 years, at which time you want to have accumulated enough money to receive a monthly annuity of $12,000 for 25 years after retirement. During the period before retirement you can earn 9% compounded annually, while after retirement you can earn 10% on your money. What annual contributions to this retirement fund will allow you to receive the $12,000 monthly annuity?

Answer 1

Number of years before retirement=40
Rate before retirement =9%

Number of periods after retirement =25*12 =300
Rate per month =10%/12
Value of retirement fund =PMT*((1-(1+r)^-n)/r) =12000*((1-(1+10%/12)^-300)/((10%/12) =1320566.7607

Number of years before retirement=40
Rate before retirement =9%
Annual contribution =Retirement/((1+r)^n-1)/r) =1320566.7607/((1+9%)^40-1)/9%) =3908.36