Question

You decide to lend your sister, who has never defaulted on a loan (ie. ρd=0), $1000 for one year. At the end of the year she agrees to pay you $1040. a)What is the nominal interest rate you and your sister agreed upon?

b)Suppose you expected the inflation rate, πe, to be 3%. What was the realrate of interest that you expectto receive?

c)However, at the end of the year,you realized that the inflation rate was actually 5%. What is the real rate of interest you actually received?

d)Are you better or worse off than you expected?

e)Now your best friend would like to borrow $1000. Unlike your sister, your best friend has bad credit because he has defaulted on many loans in the past. But he could really use your help and hepromises that he will pay you back in one year. You decide to lend to your best friend, but, because of his past defaults, you assume that he is likely to default. Therefore, you assume a ρ = 10%. Using the expected inflation rate, πe, of 3% and the real rate of interest you expected to receive above (your answer to question b), what interest rate do you charge your best friend?

Answer 1

1) At the end of the year agrees to recieve= 1040

So interest = 1040-1000=40 interest rate= 40/1000*100=4%.

2) real interest rate is calculated as the difference between interest rate and inflation rate. Interest rate=4% inflation rate= 3% . Real interest rate= 4%-3%= 1%.

3) If expected inflation rate is 5% then real interest rate= 4%-5%= -1%.

4) when inflation rate was 4% real interest rate was a positive number at 1% but when inflation rate was 5% real interest rate was a negative number that is -1%. So it is the worse condition because before it was positive and after it is negative.

5) Here, it is the 10% chance of getting the default. Therefore p=10%. So inflation rate is 3% and real interest rate is 1%. So nominal interest rate = 3+1= 4% but p=10% . So new interest rate= 4*10%= 0.4 so she would charge= 4%+ 0.4%= 4.4%.