Answer:
A. 4.02%
B. 3.49%
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%
