Question

Billy is 30 years old and has $100,000 for retirement in an IRA with 6% interest, compounded monthly, for the next 30 years. Billy wants to retire in exactly 30 years at age 60, and he can afford to put $X per month into the account starting next month and then continuing for the subsequent 359 months straight until he retires. When Billy retireS, he plans to use the entire balance in the IRA to purchase an ordinary annuity that pays monthly payments of $4,000 for his expected remaining life of 40 years. This annuity is priced so that its discount rate is 3% (compounded monthly). We ignore inflation throughout this problem. Find X, the amount Billy needs to start investing on a monthly basis to reach his retirement goal.

Answer 1

Using financial calculator
Input: PMT=-4000, N=40*12=480

I/Y= 3/12

Solve for PV as 1,117,367.06

This is the amount required at retirement.

Using financial calculator

Input FV=1,117,367.06

PV= -100000

N= 30*12=360

I/Y=6/12

Solve for PMT as 512.79

This is the monthly amount required