Question

Elissa Rump, aged 22, has decided to assert her independence and not join the Rump family businesses. Instead she is about to begin her career as a scientist for a government research organisation. Having taken a course in finance as part of her university studies, Elissa knows she should begin saving for retirement immediately.

Elissa’s retirement plan allows her to make equal yearly contributions, and it pays 9% interest annually. Upon her retirement at age 65, Elissa plans to buy a new boat, which she estimates will cost her $300 000. She also estimates that in order to live comfortably she will require a yearly income of $80 000 for each year after she retires. Based on her family history, Elissa expects to live until age 80.

When she retires, Elissa will purchase her boat in one lump sum and place the remaining balance into an account that pays 6% annual interest, from which she will withdraw her $80 000 per year, at the end of each year.

Required:

If Elissa’s first contribution is made one year from today and her last is made the day she retires, how much money must she contribute each year to her retirement fund? (Ignore tax.)

NEED HALD CALCULATIONS WITH STEP BY STEP PROCEDURE.

Answer 1

~ Step 1 : Future Value Required as on Year 43 from today (When Elissa is 65 years old)

(a) For the boat : $300,000

(b) For annuity:

N = 15

PMT = $80,000

I/Y = 6%

FV = 0

Using financial calculator, PV = $776,980

Therefore, the total amount that she will require at the age of 65 (43 years from today):

= $300,000 + $776,980

= $1,076,980

~ Step 2 : Annual Contributions required from Year 1 to Year 43 for the above Future Value:

FV = $1,076,980

PV = 0

I/Y= 9%

N = 43

Using financial calculator, we get :

PMT = $2,442.99

Therefore, Elissa must contribute $2,442.99 each year to her retirement fund.