Question

OILUUS Problem 8-7 (algorithmic) Question Help The incredible shrinking $50 bill in 1957 was worth $50, but in 2007 it is worth only $6.76. a. What was the compounded average annual inflation rate (loss of purchasing power) during this period of time? b. Fifty dollars invested in the stock market in 1957 was worth $1,988 in 2007. In view of your answer to Part (a), what was the annual real interest rate earned on this investment? a. The loss of purchasing power is - 3.92 %. (Round to two decimal places.) b. The annual real interest rate earned was %. (Round to two decimal places.) Fnter your answer in the answer box and then click Check Answer.

Answer 1

a.

FV = P *(1+i)^t

t = 2007 - 1957 = 50 yrs

FV = 6.76

P = 50

inflation rate = (6.76 / 50)^(1/50) - 1

= 0.1352 ^ 0.02 - 1

= 0.96077022 - 1

= -0.039229 ~ -3.92%

b.

Here FV = 1988, P = 50

Nominal ROR = (1988 / 50)^(1/50) -1

= 39.76 ^ 0.02 - 1

= 1.0764377 - 1

= 0.0764377 ~ 7.64%

Real rate of return = (1+nominal retrun) / (1+ inflation) -1

= (1+0.0764377) / (1+0.039229) - 1

= (1.0764377) / (1.039229) - 1

= 1.0358042 - 1

= 0.0358 ~ 3.58%