Question

An individual wants to retire in 15 years when he turns 65. He wants to have enough money to maintain his current income, which is $55,000 per year. It is assumed that a 6% annual investment rate of return and a 4% inflation rate per year. He expects that he will live to be 90 years old. He expects his raises to equal the inflation rate, approximately how much does he need at retirement to fulfill his retirement goals? ( Retirement expenses are assumed to be prepared at the beginning of each year)

A $55,000

B $2,285,195

C $1,988,957

D $99,051.89

Answer 1

Annual income required at 65th birthday = Current Income(1+inflation rate)^Number of years

= 55000(1+4%)^15

= $99,051.89

Amount required on retirement is equal to present value of all future withdrawals

Present value of growing annuity

= Amount/(r-g) *[1-{(1+g)/(1+r)}n ]

= 99051.89 + 99051.89(1+4%)/(6%-4%)*[1-{(1+4%)/(1+6%)}^24]

= 1,988,940.22

i.e. C $1,988,957 approx.

Hence, the answer is C.

Note: Number of years after retirement = 90-65 = 25

Since withdrawal is required at the beginning of each year, the present value of amount required on 65th borthday will be eual to the amount itself plus additional 24 payments in future