You are given the following US Treasury Note yield curve data:

Years to Maturity	Par Coupon YTM	Calculated Spot Rate	Calculated 1-year Forward Rate
1	5.00%	5.00%	5.00%
2	5.20%	5.21%	5.42%
3	6.00%	6.05%	7.75%
4	7.00%	7.16%	10.56%
5	7.00%

(a) Compute the five-year spot rate and forward rate assuming annual compounding. (6 marks)

(b) Explain why, for financial assets like coupon-paying bonds, it is not a good idea to value the asset using a single discount rate. (4 marks)

(c) You are given the following data for two bonds, ABC and XYZ:

Characteristic	ABC	XYZ
Market Price	101.75	101.75
Maturity Date	1-Jun-25	1-Jun-25
Call Date	Noncallable	1-Jun-20
Annual Coupon	6.25%	7.35%
Interest Payment	Semiannual	Semiannual
Effective Duration	7.35	5.4
YTM	6.02%	7.10%
Credit Rating	AA	AA

(i) Assess the magnitudes of the modified durations of ABC and XYZ, relative to their respective effective durations. (3 marks)

(ii) Compute the percentage price change forecasted for ABC and XYZ of an interest rate decline of 50 basis points over the next 6 months. (3 marks)

(iii) Suppose the actual prices at the end of 6 months were 105.55 and 104.14 for ABC and XYZ, respectively. Evaluate and explain why the actual price change would be greater for ABC and why the actual price change would be less for XYZ. (4 marks)