Consider a perpetuity that pays you $1,000,000 every 6 months. Assume that the interest rate is 5%. You want to estimate the change in the value of your perpetuity when the interest rate suddenly increases by 0.1% to 5.1%. Round your answers (but not the intermediate results) to the nearest dollar.

 

a) By how much the value of the perpetuity will change? 

 

b) If you would have estimated the change in the value of the perpetuity using the first-order Taylor approximation, by how much would your answer differ from the actual change that you were supposed to find.

 

 c) If you would have estimated the change in the value of the perpetuity using the second-order Taylor approximation, by how much would your answer differ from the actual change that you were supposed to find.

 

All interest rates are annual interest rates with semi-annual compounding unless specified otherwise. All coupon rates are annual coupon rates paid semi-annually unless specified otherwise.