Question

Today is Joan's 30th birthday. Assume that she deposits $3,400 today and $3,400 on each of her birthdays until she turns 60 (when she makes the last deposit) into an account earning 6% p.a. She plans to withdraw equal amounts each year from the time she turns 65 until she is 80. The maximum amount that each withdrawal can be is $______.

Answer 1

FV at age 61

FVAnnuity Due = c*(((1+ i)^n - 1)/i)*(1 + i )

C = Cash flow per period

i = interest rate

n = number of payments

FV= 3400*(((1+ 6/100)^31-1)/(6/100))*(1+6/100)

FV = 305625.25

FV at age 65

Future value = present value*(1+ rate)^time

Future value = 305625.25*(1+0.06)^(65-61)

Future value = 385844.84

Withdrawals

PVAnnuity Due = c*((1-(1+ i)^(-n))/i)*(1 + i )

C = Cash flow per period

i = interest rate

n = number of payments

385844.84= Cash Flow*((1-(1+ 6/100)^-16)/(6/100))*(1+6/100)

Cash Flow = 36019.03