Question 14.3: In 1924 Mr O'Leary buried $1,000 worth of quarters in his ba...
In 1924 Mr O’Leary buried \$1,000 worth of quarters in his backyard. Over the years he had always thought that the money would be a nice nest egg to give to his first grandchild. His first granddaughter, Gabrielle, arrived in 1994. From 1924 to 1994, inflation averaged 4.5\% , the stock market increased an average of 15\% per year, and investments in guaranteed government bonds averaged a 6.5\% return per year. What was the relative purchasing power of the jar of quarters that Mr O’Leary gave to Gabrielle at her birth? What might have been a better choice than his backyard investment?
Mr O’Leary’s \$1,000 are actual dollars in both 1924 and in 1994. To obtain the real 1924 dollar equivalent of the \$1,000 that Gabrielle received in 1994, we would strip 70 years of inflation out of those dollars. This loss of purchasing power caused by inflation can be calculated as follows:
Real 1924-based dollars in 1994 = (Actual dollars in 1994 (P/F,f, 1994-1924) = \$1,000(P/F, 4.5\%, 70) = \$45.90
On the other hand, if Mr O’Leary m had put his \$1,000 in the stock market in 1924, he would have made baby Gabrielle an instant multi-millionaire by giving her \$17,735,000 . We calculate this as follows:
Actual dollars in 1994 = (Actual dollars in 1924) (F/P, i, 1994-1924) = \$1,000(F/P, 15\%, 70) = \$17,735,000
At the time of Gabrielle’s birth, that \$17.7 million translates to \$814,069 in 1924 purchasing power. This is quite a bit different from the \$45.90 in 1924 purchasing power calculated for the unearthed jar of quarters.
Real 1924-based dollars in 1994 = (\$17,735,000)(P/F, 4.5\%, 70) = \$814,069
Mr O’Leary was never a risk taker, so it is doubtful he would have chosen the stock market for his future grandchild’s nest egg. If he had chosen guaranteed government bonds instead of his backyard, by 1994 the investment would have grown to \$59,076 (actual dollars)-the equivalent of \$2,7 12 in 1924 purchasing power.
Actual dollars in 1994 = (Actual dollars in 1924)(F/P, i, 1994-1924)
= \$1,000(F/P, 6\%, 70) = \$59,076
Real 1924-based dollars in 1994 = \$59,076(P/F, 4.5\%, 70) = \$2,7 12