Question

General price inflation is estimated to be 3% for the first 5 year, 5% for the 5 years after that, and 8% the following 5 years. If you invest $10,000 at 10% per year for those 15 years:

A. What is the future worth of your investment in year 15 in actual dollars? (ANS: $41,772.48)

B. What is the future worth of your investment in year 15 in year-0-dollars? (ANS: $19,214.95)

C. What is the average inflation for those 15 years? (ANS: 5.31%)

Answer 1

A. Future worth of investment in actual dollars = =PV*(1+r)^n = 10,000*(1+0.10)^15 = $41,772.48

B. Future worth in Zero dollars : For first five years, real rate = (0.10-0.03)/1.03 = 0.06796, So FV = 10,000*(1+0.06796)^5 = 13,892.40.

For the next five years, reat rate = (0.10-0.05)/1.05 = 0.047619, So FV = 13,892.40 *(1+0.047619)^5 = 17,530.49623

For the last five years, real rate = (0.1-0.08)/1.08 = 0.0185185, So FV = 15,530.49623*(1+0.0185185)^5 = $19,214. 94

So 0 dollar FV = $19,214.95 (Small difference due to decimals)

C: Average Inflation = (3%*5 +5%*5 +8%*5)/15 = 5.33% (small differce due to decimals)