Question

Mrs.McNamara just turned 44 and is beginning to plan for her retirement. She would like to make annual contributions to a retirement fund beginning with X on her 45th birthday and increasing by $500 each year until her last contribution on her 64th birthday.

These contributions should fund annual retirement checks beginning with $50,000 on her 65th birthday and increasing by 5% each year until her last retirement check issued on her 84th birthday. The fund will earn interest at the nominal rate of 10% convertible semiannually.

Determine which of the following is closest to the minimum X needed to ensure that Mrs. McNamara's retirement goals are met.

Ans: At least $6700, but less than $7100.

Answer 1

At retirement time: nper=20, PMT=50000 and will 5% each year, EAR (rate)= (1+10%/2)^2-1=10.25%, PV=?

It means at age of 64 with her last deposit she should achieve $593438.59

Now, if you invest 0 on 45th, $500 on 46th, $1000 on 47th , value of those amount on 64th birthday @10.25% becomes $189886.43

So, from deposit of X for the 20 year should become= (593438.59-189,886.43)= $403552.16

Hence, value of X is $6848.37 i.e. At least $6700, but less than $7100.