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Suppose that I ask you to lend me $200 for one year at a 5% promised...

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Finance

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 ensureyourself an expected return of 5%?

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3.6 Ratings (430 Votes)

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%
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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 ensureyourself an expected return of 5%?

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