Question

Victor is spending HKD300,000 per year and is quite satisfied with the present living lifestyle and standard. He is now 38 and plans to retire at age 60. He believes he can live up to age 85. He wants to keep 80% of the current living lifestyle and standard after retirement.

Victor would like all the money for retirement to be ready when he retires. He also would like the retirement money for spending in a year to be ready at the beginning of every year. He plans to start saving for the retirement reserve with an equity unit trust fund of 10% annual rate of return. Average expected annual rate of return during his retirement period is 6%. Assume the average long term inflation is 4% p.a.

a. What is the required annual expenditure at the time when Victor retires at age 60?

b. What is the total amount of money required for 25 years after Victor’s retirement? (at the beginning of age 60)

c. How much should Victor save at the beginning of each month from now on until the age of 60 in order to meet the required amount at (c)?

Answer 1

a.

years up to retirement = 60 - 38 = 22 year

annual expenditure at the time of retirement = current expenditure * ( 1 + i )ⁿ = (300000*0.8) ( 1+0.04)²² = HKD 568780.51

Where,

n = years up to retirement

i = inflation rate

b.

here use excel

amount require at beginning of retirement = =PV(rate,nper,pmt,fv,type)

= pv(0.01923,25,568780.51,0,0)

= HKD 11205599.13

where

rate = inflation adjusted rate of return

nper = years after retirement

pmt = annual expenditure at the time of retirement

fv = future value

inflation adjusted rate of return =[ (1+r) / (1+i)] - 1 = (1.06 / 1.04) - 1 = 1.0192 -1 = 0.0192

where r =return of investment

i =inflation rate

c.

value need at retirement after 22 year = future value (FV) = HKD 11205599.13

nper = total month = 22*12 =264 month

monthly investment return(rate) = 0.10/12 = 0.008333

PV= present value = 0

type = 1 because of beginning

monthly saving need = =pmt(rate,nper,pv,fv,type)

=pmt(0.008333,264,0,11205599.13,1)

= HKD 11659.62

hence Victor save HKD 11659.62 at the beginning of each month from now on until the age of 60 in order to meet the required amount of 11205599.13