Question

The incredible shrinking​ $50 bill in 1957 was worth​ $50, but in 2007 it is worth only ​$. 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 ​$ in 2007. In view of your answer to Part​ (a), what was the annual real interest rate earned on this​ investment?

Answer 1

A. 4.02%

B. 3.49%

Step-by-step explanation:

a. Computation of the compounded average annual inflation rate​ during this period of​ time

Using this formula

Annual inflation rate=FV/ P *(1+i)^t

Where,

t = 2007 - 1957 = 50 yrs

FV = 6.42

P = 50

Let plug in the formula

Annual inflation rate = (6.42 / 50)^(1/50) - 1

Annual inflation rate= 0.1284 ^ 0.02 - 1

Annual inflation rate= 0.959779 - 1

Annual inflation rate= -0.0402208 *100%

Annual inflation rate=4.02%

b. Computation of the annual real interest rate earned on this​ investment

First step is to find the Norminal ROR

Using this formula

Norminal ROR

= FV/ P *(1+i)^t

Where

FV = 1998

P = 50

let plug in the formula

Norminal ROR = (1998 / 50)^(1/50) -1

Norminal ROR= 39.96 ^ 0.02 - 1

Norminal ROR= 1.076545 - 1

Norminal ROR= 0.0765457 *100

Norminal ROR= 7.65%

Last step is to calculate for annual real interest rate earned using this formula

Annual real interest rate earned = (1+ Nominal ROR) / (1+ Inflation) -1

Let plug in the formula

Annual real interest rate earned=(1+0.0765457) / (1+0.0402208) - 1

Annual real interest rate earned= (1.0765457) / (1.0402208) - 1

Annual real interest rate earned= 1.034920 - 1

Annual real interest rate earned= 0.0349*100

Annual real interest rate earned=3.49%

Therefore the Annual inflation rate will be 4.02% while Annual real interest rate earned will be 3.49%