Question

Suppose that there is compound interest at an annual inflation adjusted rate of 1.7% and that the annual rate of inflation is 2.8%.

• Find the force of interest corresponding to the stated rate of interest.  (Round your answer to four decimal places.)
• Find the inflation-adjusted force of interest corresponding to the real rate of interest.    (Round your answer to four decimal places.)
• In general, what can you say about the difference between the force of interest and the inflation-adjusted force of interest? A, B or C?

A. If the actual rate of interest is higher than the adjusted rate of interest, the force of interest for the actual interest is lower.

B. If the actual rate of interest is higher than the adjusted rate of interest, the force of interest for the actual interest is higher.   

C. The force of interest is the same in both cases.

Answer 1

(1)

Force of Interest = In (1+r)

Where, r is Interest Rate (Return)

Inflation Adjusted Rate =

Here, Inflation Adjusted Rate = 1.7%

       Inflation Rate = 2.8%

So           1.7 = [(1+ r)/(1=2.8)] – 1

=> r = 9.26%

Putting the value of r in Force of interest

Force of Interest = In (1+0.0926)

                                   = In (1.0926)

                                   = 0.088560

Force of Interest   = 8.8560%

So, Force of Interest corresponding to the stated rate of interest = 8.8560%

(2)

Force of Interest = In (1+r)

Where r is interest rate = 1.7%

Force of Interest = In (1+0.017)

                                   = In (1.017)

                                   = 0.016857

Force of Interest   = 1.6857%

So , Inflation-adjusted Force of Interest corresponding to the real rate of interest = 1.6857%

(3)

B. If the actual rate of interest is higher than the adjusted rate of interest, the force of interest for the actual interest is higher.