12. For the 5-year bond in exercise 11, start with prices calculated at 6% and 10%:

(a) Develop graphs of these bond prices over time using (2.18)

(b) Show that in the case of the 6% valuation, that the successive ratios of the bond’s write downs, defined as the quantities Pj=2ð0:06Þ  Pð jþ1Þ=2ð0:06Þ, have a constant ratio of 1:03.

(c) Show similarly that for the 10% valuation, the successive ratios of the bond’s write ups, defined as the quantities Pð jþ1Þ=2ð0:10Þ  Pj=2ð0:10Þ, have a constant ratio of 1:05.

(d) Derive algebraically using (2.16), the general formula for a write up or write down and show that the common ratio is 1 þ i 2 , where i denotes the investor’s yield.