Question

Al and Amanda meet with Shino, the banker, to work out the details of a mortgage. They all expect that inflation will be 3 percent over the term of the loan, and they agree on a nominal interest rate of 7 percent. As it turns out, the inflation rate is 4 percent over the term of the loan. a. What was the expected real interest rate? b. What was the actual real interest rate? c. Who benefitted and who lost because of the unexpected inflation?  

Answer 1

a)

Given

Nominal interest rate =i=7%

Inflation rate=f=3%

Expected real interest rate=r=?

We know that

(1+r)=(1+i)/(1+f)

or

r=(1+i)/(1+f)-1=(1+7%)/(1+3%)-1=3.88%

b)

If new inflation rate,f, is 4%. Then

Actual real interest rate=r=?

We know that

(1+r)=(1+i)/(1+f)

or

r=(1+i)/(1+f)-1=(1+7%)/(1+4%)-1=2.88%

c)

In this case actual real rate of interest is lower than the expected real interest rate. So,

Shino, the banker is at loss due to unexpected inflation.

Al and Amanda (borrrowers) are benefitted due to unexpected inflation.