Question

Risk is a key characteristic to understanding interest rates.   Interest rates are key to the loanable funds market. The goal of this exercise is to better understand how risk directly factors into interest rates.   Let's try this example.  

Pretend you are a bank that has no costs whatsoever.   Further, you’re a non-profit bank whose only goal is to break even. Explain what you need to set as your interest rate in the following situations in order to break even.

You have 10 people who are going to each borrow $1000. You expect 1 out of these 10 will default on their loan, and pay you back nothing.  (Hint, you need to get back $10,000 in money from 9 people. Each will have to pay $10,000/9=$1,111. That means they would have to pay you $111 interest on $1000 loan. To calculate the interest rate ((1111-1000)/1000) = 11% would be the interest rate this group would have to pay.)

Question. You have 100 people who are going to each borrow $1000. You expect 1 out of these 100 will default on their loan, and pay you back nothing.

Who will pay a higher interest rate?  Why? How much of this difference in interest rate is due to the profit motive?

Can this help explain the paradox that the poor (Countries or People), who can less easily afford higher interest rates are often charged a higher rate? What do you think this does for long term growth for these populations?

Answer 1

Soln.

As per the above example in which one out of ten members default in repaing loan interest rate will be 11% charged by the bank to nulify the risk, where if as per the question statement one out of hundrad members default then each has to pay 100000/99 = 1010.10 each which means interest rate of 10.10%.

So the earliar has to pay 0.90 perecntate point highier interest and all is just because thatit has more highiter rate of defaulters as compare to the later one.

if a country has more defaulters then its population has to bear higher rate of interest as shown with above example then it will adversaly effects the growth rate of the country and even in the long run its effects can be seen clearly as marginal efficiency of capital will reduce for the production functions due to higher cost of capital and even if we compare the defaulters out of 100 so in the earliar one rate is much higher which means it has less member who contribute in the growth of the nation (like 90 in the earliar and 99 in the later).

(Note: if any one has any doubt in the explaination then he/she may as further clarification in the comment section)