# 经济学作业代做 ECON 4784 Prof. Francisca Antman

## Prof. Francisca Antman

### Exercise 10—Interest Rates--SOLUTIONS  经济学作业代做

Suppose that a moneylender operates in a competitive credit environment where the opportunity cost of funds is 10%. Also assume that only 50% of loans are paid back with interest and the

remainder of the borrowers default.

### a. Find the interest rate the money-lender charges his clients.

Zero profit condition states: p(1+i)L – (1+r)L = 0, where only fraction p loans will be paid back  (probability of repayment=p).

This implies: i = (1+r)/p – 1.

If p=1/2 and r = .10, i has to be 120% to cover the risk of default! (2.2-1 = 1.2)  经济学作业代做

b.If a rural borrower took out a \$100 loan for one year, how much would he have to pay back at the end of the year, including interest and principal? (You may assume interest compounds annually.)

100*(1+1.2) = \$220

c.What would the interest rate be if all loans were paid back with certainty?

### i = r which in this case is 10%  经济学作业代做

d.What would happen to the gap between the interest rate and the lender’s opportunity costs if there were a rise in the probability of repayment? What if there were a drop in the probability of repayment?

If there were a rise in probability of repayment, i would fall closer to r, so the gap (i-r) would fall.

If there were a drop in probability of repayment, i would rise further to be further away from r, so  the gap (i-r) would rise.经济学作业代做 