Suppose you borrow $100 of principal that must be repaid at the end of two years, along with interest of 4 percent per year. If the annual inflation rate turns out to be 8 percent,

(a) What is the real rate of interest on the loan?

(b) What is the real value of the principal repayment?

5gf

(a)

-4%

To calculate the real rate of interest and the real value of the principal repayment, we need to take into account the inflation rate.

(a) The real rate of interest measures the purchasing power of the interest earned after considering the effects of inflation. It is calculated by subtracting the inflation rate from the nominal interest rate. In this case, the nominal interest rate is 4 percent and the inflation rate is 8 percent.

Real rate of interest = Nominal interest rate - Inflation rate
Real rate of interest = 4% - 8%
Real rate of interest = -4%

Therefore, the real rate of interest on the loan is -4%.

(b) The real value of the principal repayment indicates the purchasing power of the amount repaid after considering the effects of inflation. It is calculated by adjusting the principal repayment for inflation.

To find the real value of the principal repayment after two years, we need to adjust the $100 for the inflation rate of 8 percent. We can use the formula:

Real value of the principal repayment = Principal repayment / (1 + Inflation rate)^2

Real value of the principal repayment = $100 / (1 + 8%)^2
Real value of the principal repayment = $100 / (1 + 0.08)^2
Real value of the principal repayment = $100 / 1.08^2
Real value of the principal repayment = $100 / 1.1664
Real value of the principal repayment = $85.82 (rounded to the nearest cent)

Therefore, the real value of the principal repayment is approximately $85.82.