Question

# Today is Joan's 30th birthday. Assume that she deposits \$3,400 today and \$3,400 on each of...

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 \$______.

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

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