Inflation Adjusted Savings

Question

You need $75,000 in today's dollars for a purchase in 3 years. You expect that your savings will earn 7% compounded annually, and inflation will be 4%. You will make 3 equal annual deposits starting at the end of the year. What is the amount of your first payment? How much will you have at the end of the 3 years?

Answer 1

This is a forward, backward forward type question. With 4% inflation to buy what you buy today for 75,000 you will need. 75,000*(1+4%)³. or 84,364.80. 84,364.8 brought back to Present Value at 7% is

PV= 84,364.80*(1/(1.07))³ = 68,866.81. The Annuity equivalent of 68,866.81 is given by the relationship

PV=PMT*ß(i,N) where ß is available from any loan table or can be calculated as

ß =(1/i)(1-(1/(1+i)^N) her, i=7% and N=3 so ß=(100/7)(1-(1/(1.07)³) = (100/7)(1- .816297) =2.624316

so PMT= PV/ß= 68,866.81/2.624316= 26,241.81 in 1 year, 2 years and 3 years

Hope this helps