Mrs.McNamara just turned 44 and is beginning to plan for her retirement. She would like to...

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.

Expert Solution

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.

jeff jeffy answered 2 months ago

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