Question

Frank is lending $1,000 to Sarah for two years. Frank and Sarah agree that Frank should earn a 1 percent real return per year. Instructions: Enter your responses as as whole numbers. a.The CPI (times 100) is 100 at the time that Frank makes the loan. It is expected to be 117 in one year and 136.9 in two years. What nominal rate of interest should Frank charge Sarah? The nominal rate of interest charged should be %. b. Suppose Frank and Sarah are unsure what the CPI will be in two years. How should Frank index Sarah's annual repayments to ensure that he gets an annual 1 percent real rate of return. Frank should charge Sarah % the inflation rate.

Answer 1

a) 18%

b) if Frank and Sarah are unsure about future inflation rate, they can agree on a variable interest rate. For e.g. this year the inflation rate was 17%, so the interest charged is 18%. If next year the interest rate is 15%, then the interest charged should be 16%.

the formula that they can use to calculate inflation rate is:

• for calculating the first year's inflation rate = [(CPI₁ - CPI₀) / CPI₀] x 100
• for calculating the second year's inflation rate = [(CPI₂ - CPI₁) / CPI₁] x 100

Step-by-step explanation:

principal $1,000

real return = 1%, that means that Frank will earn inflation rate + 1%

since the CPI increases by 17% every year, then Frank must charge 17% + 1% = 18%