Question

10a. If the expected default rate on a credit card is 8.5% and the risk-free rate is 3.25%, what interest rate must a financial institution charge on the credit card in order for its expected return to equal the risk-free rate? If the financial institution assumes a 0% recovery rate in the event of default, what interest rate will the financial institution charge?

b. If the expected default rate on a 1-year home equity loan is 2.5% and the financial institution expects to recover 75% of the total loan return in the event of default, what rate must a financial institution charge on the automobile loan in order for its expected return to equal the risk free rate of 3.25%?

Answer 1

1.

1*(1+rf)=pd*recovery rate*1*(1+r)+(1-pd)*(1+r)
1*(1+3.25%)=8.5%*0%*1+(1-8.5%)*(1+r)
=>r=(1+3.25%)/(1-8.5%)-1
=>r=12.84%

2.

1*(1+rf)=pd*recovery rate*1*(1+r)+(1-pd)*(1+r)
1*(1+3.25%)=8.5%*75%*1*(1+r)+(1-8.5%)*(1+r)
=>r=(1+3.25%)/(8.5%*75%+1-8.5%)-1
=>r=5.49%