Question

Question 1

If a real rate of return of 6.9% per year is desired on a loan, and the rate of inflation is averaging 3.8% per year, then what combined interest rate should be charged by the lender? Enter your answer as a percentage and round to three significant figures.

Question 2

The cost of a first-class stamp in 1970 was 7 cents. By 2015, the cost of a stamp had increased to 47 cents. What was the average rate of inflation for a stamp over that period of time? Enter your answer as a percentage and round to three significant figures.

Answer 1

Question 1)

Real rate of return desired (D) = 6.9% = 0.069

Rate of inflation (I) = 3.8% = 0.038

Let the rate of interest = r%

From the formula to calculate interest including inflation

(1+D) = (1+r)/(1+I)

(1+0.069) = (1+r)/(1+0.038)

1+r = 1.1096

r = 0.096

Hence rate of interest is 9.60%

Question 2)

cost of postage stamp in 1970 (C)= 7 cents

Cost of postage stamp in 2015 (F) = 47 cents

Let the rate of inflation is = I%

Number of years (n)= 45 years

From calculations

F = C*(1+I)^n

47 = 7*(1+I)^45

Upon solving we get

1+I= 1.04322

Hence I = 0.04322

Hence inflation (I) = 4.322% per year