Question

suppose you wish to retire forty years from today. you determine that you need $50,000 per year, with the first retirement amount withdrawn after one year from the day you retire. assume a nominal interest of 6% compounded quarterly and that you will need the retirement amount for 25 years after retirement. draw the cash flow and calculate how much you must deposit each quarter in your account starting one quarter from today until retirement.

Answer 1

No. of quarterly deposits = 40 * 4 = 160

i = 6% / 4 = 1.5% per quarter

No. of yearly withdrawal = 25

Effective interest rate = (1+0.015)^4 -1

= (1.015)^4 -1

= 0.06136355 ~ 6.1364%

Value of withdrawal at EOY 40 = 50000*(P/A,6.1364%,25)

= 50000 * ((1 + 0.061364)^25-1)/(0.061364 * (1 + 0.061364)^25)

= 50000 * ((1.061364)^25-1)/(0.061364 * (1.061364)^25)

= 50000*12.619336

= 630966.80

Amount of quarterly deposits = 630966.80 * (A/F,1.5%,160)

= 630966.80 * 0.015/((1 + 0.015)^160-1)

= 630966.80 * 0.015/((1.015)^160-1)

= 630966.80 * 0.00152618

= 962.97 ~ 963 (Nearest whole dollar)

CFD