Question

Frank is lending $1,000 to Sarah for two years. Frank and Sarah agree that Frank should earn a real return of 1 percent per year.

Instructions: Enter your responses 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 about 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 rate of return?

Frank should charge Sarah ____ %  (Click to select)  more than, equal to, less than, the inflation rate.

Answer 1

a) Frank wants the real value of his loan to be $$1,020.1 at the end of the two year loan period in order for him to realize a 1% real rate of return per year.

Real value of loan in 2 years = $1,000 x (1.01)^2 = $1,020.1

where r is the annual real rate of return.

Inflation, will act to reduce the real value of his loan. In order to achieve his objective, he will have to charge a nominal rate of interest that more than offsets it as follows.

Real value of loan in 2 years = ($1,000 x (1 + rn)^2)/1.369 = $1,020.1,

Where rn is the nominal rate of interest expressed as a decimal.

Solving for rn gives:

(1 + rn)^2 = $1020.1 x 1.369/$1,000 = 1.39651

1 + rn = 1.39651^0.5 = 1.18174

rn = .18174

The nominal rate of interest charged should be 18.174% or expressed as an integer, 18%.

b) If the inflation rate is uncertain, Frank should index Sarah's annual repayments to the actual inflation rate realized over each year. Frank should charge Sarah 1% more than the inflation rate.