Question

You have been hired as a financial consultant by Independent Investment Partners, with offices in all 50 states. Your first assignment is to advice a client, Jane Smith, who is considering whether to accept an early retirement package offered by her firm. Ms. Smith currently earns a $55,000 and she is 40 years old. She is good health and expects that she could work for another 30 years before retirement. If she rejects the early retirement offer and continues to work for her company, her annual salary could increase at the rate of 3.5% per year. She wants you to advise her whether she should accept the early retirement offer or not. Your firm could guarantee her a rate of return of 7% annually on her investments. Answer the next three questions in order to explain her options to her.

A -

What would be Jane’s lump sum payment if she accepts the early retirement offer?

B-

If Jane decides to save only 10% of her lump sum (early retirement) payment and she is able to earn a guaranteed return of 12.5%, how much would she accumulate from her savings in 30 years when she turns 70 years old? SHOW WORK or excel inputs or financial calculator inputs.

C-

How much could Jane withdraw in equal amount over the next 20 years (i.e. to her 90^th birthday) from her savings? SHOW WORK

Answer 1

A -

Jane will accept the early retirement only if the present value of her future earnings is given to her in retirement

Lump sum amount = 55000*1.035/1.07+55000*1.035^2/1.07^2+.... +55000*1.035^30/1.07^30

=55000*1.035/1.07 * (1-(1.035/1.07)^30)/ (1-1.035/1.07)

=$1,026,731.18

B

If 10% of the above amount i.e. $102673.12 is saved , after 30 years, the amount will be

= 102673.12*1.125^30

= $3515866.90

C  

Continuing from part B above and assuming end of year withdrawals

Annual amount that can be withdrawn (A) is given by

A/1.125+A/1.125^2+A/1.125^3+.....+A/1.125^20 = 3515866.90

=> A/0.125*(1-1/1.125^20) = 3515866.90

=> A = $485526.22