Using excel, check the validity of these five rules for Duration.

1. The duration of a zero-coupon bond equald its time to maturity

2. With time to maturity and yield to maturity held constant, a bond's duration and interest rate sensitivity are higher when the coupon rate is lower

3. With the coupon rate held constant, a bond's duraton and interest rate sensitivity generally increase with time to maturity. Duration always increases with maturity for bonds selling at par or at a premium to par.

4. With other factors held constant, the duration and interest rate sensitivity of a coupon bond are higher when the bond's yield to maturity is lower.

5. The duration of a level perpituity is: (1+y)/y

The initial bond yield is 6%. These durations are for several bonds, all paying annual coupons.

Please show how each of the 5 rules hold true through excel, using the example.

Coupon Rates (% per year) Years to Maturity 6 8 10 1.000 10 20 Infinite (perpetuity) 1.000 4.611 8.281 13.216 17.667 4.465 7.802 12.158 17.667 1.000 4.342 7.445 11.495 17.667 1.000 4.237 7.169 11.041 17.667 17.667 m E5 4 4.237 fx B C D 1 Durations of annual coupon bonds (initial bond yield = 6%) 2 Coupon Rates (% per year) 3 Years to Maturity 4 10 5 10 00 vou 4.611 8.281 13.216 17.667 20 4.465 7.802 12.158 17.667 4.342 7.445 11.495 17.667 4.2371 7.169 11.041 17.667 Infinite (perpituity) o ? Coupon Rates (% per year) Years to Maturity 6 8 10 1.000 10 20 Infinite (perpetuity) 1.000 4.611 8.281 13.216 17.667 4.465 7.802 12.158 17.667 1.000 4.342 7.445 11.495 17.667 1.000 4.237 7.169 11.041 17.667 17.667 m E5 4 4.237 fx B C D 1 Durations of annual coupon bonds (initial bond yield = 6%) 2 Coupon Rates (% per year) 3 Years to Maturity 4 10 5 10 00 vou 4.611 8.281 13.216 17.667 20 4.465 7.802 12.158 17.667 4.342 7.445 11.495 17.667 4.2371 7.169 11.041 17.667 Infinite (perpituity) o