Question

Question 1 REAL vs. NOMINAL INTEREST RATES A farming couple noticed that the suburbs kept moving their way. Buying land on the city side of the farm seemed like a good investment. 1,000 acres were for sale for $1 million, $1,000 per acre. They borrowed $1 million for one year at 5% interest. At the end of the year, they repaid the loan (principal and interest). They funded the loan repayment by selling land, including some of their equally valuable farmland - if necessary. At the end of the year, land sold for $1,105.263 per acre. The nominal interest rate was 5%. What was their real interest rate? (Explain.)

Answer 1

Inflation rate=(Sale price-Purchase Price)/Purchase price

Total sale price=1105.263*1000=$1105263

Inflation rate=$\pi$=(1105263-1000000)/1000000=10.53%

Nominal Interest rate=i=5%

Real interest rate=r=?

Fisher equation suggests that

(1+i)=(1+$\pi$)*(1+r)

or

r=(1+i)/(1+$\pi$)-1

r=(1+5%)/(1+10.53%)-1=-5.00%