A young engineer on his twenty-fifth birthday decides to accumulate the equivalent of $100,000 by his sixty-fifth birthday, but is concerned about the effects of inflation on the pur- chasing power of $100,000. 157 CHAPTER 6 Geometric Gradient: The Constant Percentage Increment (a) If he assumes that inflation will increase the price of the goods and services he normally buys (thus reducing the purchasing power of the dollar) by 6 percent compounded annually, how much money will he have to accumulate in order to have the same pur- chasing power 40 years from now that $100,000 has at the present time? (Ans. $1,029,000) (b) If he starts his savings program with a deposit now on his twenty-fifth birthday, and con- tinues making equal annual deposits on each birthday including his sixty-fifth, how much should he deposit annually in order to accumulate the amount found in (a) above if his savings draw 9 percent interest compounded annually? (Ans. $2,599) (e) The young engineer reasons that his salary should be increasing as time goes on, and it makes more sense for him to start depositing a small amount in the earlier years, with increasing deposits in later years. He estimates that his salary will increase by 8 percent per year, and decides to increase the amount of his deposits by that percentage each year also. How much should he deposit the first year in order to reach the sum found in (a) above? (Ans. $908.90) (d) Same as (c), but now find the amount of the last deposit made on his sixty-fifth birthday? (Ans. $19,750)