Question

Suppose that I ask you to lend me $200 for one year at a 5% promised interest rate. You believe that I will fully pay you the $210 with 95% probability; that I will only repay $100 with 1% probability; and that I will repay nothing with 4% probability. What promised interest rate should you have charged to ensure yourself an expected return of 5%?

Answer 1

210	0.95	199.50
100	0.01	1.00
0	0.04	-
Amount expected to be received after one year		200.50
Interest amount (200.50-200)		0.5
Expected Return (0.50/200)*100		0.25%

.

220	0.95	209.00
100	0.01	1.00
0	0.04	-
Amount expected to be received after one year		210.00
Interest amount (210-200)		10
Expected Return (10/200)*100		5%

.

To an earn an expected return of 5% , we have recover $220 at the end of year.

So , promised rate of return that we should charge = (220-200)/200 * 100

= 20/200 * 100

= 10%