Question

How much do you have to deposit today in order to allow 7 annual withdrawals, beginning at the end of year 17, with a first withdrawal of $2123 and with subsequent withdrawals decreasing at the rate of 3% over the previous year’s withdrawal? Assume an interest rate of 9% compounded annually.

Answer 1

First we compute the Present Worth (PW) of the 7 withdrawals starting EOY 17, at beginning of year 17 (EOY 16).

Note that

(i) Starting beginning of year 17, Period 1 corresponds to year 17, Period 2 corresponds to year 18, and so on.

(ii) PV Factor for year N = (1.09)^-N

(iii) Withdrawal in year (N+1) = Withdrawal in year N x 0.97

Period	Withdrawal ($)	PV Factor @9%	Discounted Withdrawal ($)
	(A)	(B)	(A) x (B)
1	2,123	0.9174	1,948
2	2,059	0.8417	1,733
3	1,998	0.7722	1,542
4	1,938	0.7084	1,373
5	1,879	0.6499	1,222
6	1,823	0.5963	1,087
7	1,768	0.5470	967
		PW ($) =	9,872

Today's deposit ($) = 9,872 / (1.09)¹⁶ = 9,872 / 3.9703 = 2,486.46