Question

Your friend is celebrating her 25th birthday today and wants to start saving for her
anticipated early retirement at age 55. She wants to be able to withdraw $10,000 from
her savings account on each birthday for 10 years following her retirement, the first
withdrawal will be in her 56th birthday. She wants to make equal, annual payments on
each birthday in a new savings account she will establish for her retirement fund. The
account pays 8 per cent interest per year.

If she starts making these deposits on her 26th birthday and continues to
make deposits until she is 55 (the last deposit will be on her 55th birthday),
what amount must she deposit annually to be able to make the desired
withdrawal on retirement?

Suppose your friend has just inherited a large sum of money. Rather than
making equal payments, she has decided to make one lump-sum payment
on her 26th birthday to cover her retirement needs. What amount would
she have to deposit?

Answer 1

The first step is to find the size of the retirement fund from which $ 10,000 can be withdrawn each year for a period of 10 years. It is assumed that the savings account will pay 8% interest per year during the withdrawl period. The size of the retirement fund is found using present value of annuity equation.

Size of the retirement fund = $ 67,100.81 $ 67101

Thus the account must have $ 67101 at the time of 56th birthday so that $ 10000 can be withdrawn each year.

The annual payments to be made on each birthday is found using the future value of annuity equation.

Annual payment equals $ 592.33

Thus the friend must deposit $ 592.33 each year to reach the retirement goal.

The lump sum payment to cover the retirement needs is found using the future value of investment equation.

Lump-sum payment to cover the retirement needs = $ 6668.32