You setup a college fund for your child with 200000 Assume t

You setup a college fund for your child with {200.000. Assume the money earns an annual rate of 4.8% compounded quarterly. Your child will make quarterly withdrawals from the fund over a 5 year period. What equal amount can your child withdraw each quarter so that the balance is reduced to zero at the end of the 5 year period. What is the maximum withdrawal your child could make each quarter so that the $ 200,000 balance never decreases. (This is much easier than it sounds)

Solution

The formula to be used here is p = (Pr)/[1-(1+r)^-n] , where p is the periodic payment, P is the present value, r is the rate of interest per period, and n is the number of periods. Here,P = $ 200000, r = (4.8/100)*1/4 = 0.012 and n = 4*5 = 20. Then, we have p = (200000*0.012)/[ 1-(1+0.012)^-20] = 2400/[1-0.787752427] = 2400/0.212247572 = $11307.55 ( on rounding off to the nearest cent).

In a case of perpetual payment, the present value of the amount deposited does not decrease. The formula to be used here, is p = Pr, where p is the periodic payment, P is the present value and r is the rate of interest per period. Here, p = 200000*0.048/4 = 200000*0.012 = $ 2400. Thus, $ 2400 can be withdrawn per quarter, without reducing the balance of $ 200000 in the college fund