# Equal Payment Series

The question is: A man is planning to retire in 20 years. Money can be deposited at 8%, compounded monthly. It is estimated that the future general inflation rate will be 3% compounded annually. What deposit must be made each month until the man retires so that he can make annual withdrawals of $20000 in terms of actual dollars over the 15 years following his retirement? (Assume that his first withdrawal occurs at the end of the first year after his retirement) My approach is: $$i = (1 + \frac{0.08}{12})^{12} = 0.082$$ $$P = 20.000(P|A, 0.082, 15)(P|F, 0.082, 20) = 34966.04$$ Now to find the deposit, in terms of constant dollars first I calculate inflation free interest rate $$(1+i^{'})(1+ \frac{0.03}{12}) - 1 = \frac{0.08}{12}$$ $$i^{'}= 0.00415$$ I am not sure about this last equation, could anyone please justify or correct it? $$A = 34966.04(A|P, 0.00415, 20)$$ Thank you. • For the 15 years into retirement, are the assumptions on interest rates and inflation rates the same? Also what do the symbols$P|A$,$P|F$,$A|P\$ represent here? – Alecos Papadopoulos Mar 28 '15 at 0:46