Question

Arnold Atkinson wants to retire in 20 years at age 65. He has determined that he will need a capital sum of $2,784,000 at that time to provide his retirement income. He presently has a retirement plan with a balance of $350,000, to which he will add $25,000 per year. Phil assumes that his preretirement and postretirement rates of return will be 8%, and that inflation will average 3%. He will not consider Social Security benefits in his planning. He expects to live to at least age 80 but wants to use age 95 for all calculations. How much will he accumulate for retirement if no changes are made?

Second Part- Concering Arnold, how much more would he have to invest annually to meet his goal?

Answer 1

Present value of all the contribution he made = 25,000*PVIF(Interest = 8%, periods = 20)

= 25,000*9.82 = 245,500

Amount accumulated for the retirement = Future value of (350,000 + 245,500)

= 595,500*(1.08)^20 = 2,775,600

Additional accumulated amount needed at the time of retirement = 2,784,000 - 2,775,600 = 8,400

To get this additional 8,400 he will have to increase his annual investment by 8400/ PVIF(Interest = 8%, periods = 20)

= 8400/9.82 = 855.4