Suppose you decide to take out the $1 million 30-year fixed rate mortgage at 4%.

How much money money will you pay in interest in the 181st payment (units: dollars)?

 

 

The current 6-month short rate sits at 3% per year. The mean growth rate of the short rate is 3%; the volatility of short rate growth is 25%. 

What would be the 6-month short rate in the up state at time t=0.5 (units: % per year)?

 

 

 

The current 6-month short rate sits at 3% per year. The mean growth rate of the short rate is 3%; the volatility of short rate growth is 25%. 

What would be the 6-month short rate in the down state at time t=0.5 (units: % per year)?

 

 

The current 6-month short rate sits at 3% per year. The mean growth rate of the short rate is 3%; the volatility of short rate growth is 25%. 

Consider a 1-year floater indexed to the short rate with a face value of $100.

What is the payout to this floater at time t=0.5 (units: dollars)?

 

 

The current 6-month short rate sits at 3% per year. The mean growth rate of the short rate is 3%; the volatility of short rate growth is 25%. 

Consider a 1-year floater indexed to the short rate with a face value of $100.

What is the payout to this floater at time t=1.0 if the up state is realized at time t=0.5 (units: dollars)?