1. Following are U.S. Treasury benchmarks and their clean prices on September 4, 2020:

Notes/ Bonds	CUSIP	Maturity Date	Coupon Rate	Price (decimals)
2-Year	91282CAG6	08/31/2022	0.125%	$99.9609
3-Year	91282CAF8	08/15/2023	0.125%	$99.8516
5-Year	91282CAJ0	08/31/2025	0.250%	$99.7539
7-Year	91282CAH4	08/31/2027	0.500%	$99.9766
10-Year	91282CAE1	08/15/2030	0.625%	$99.1016
20-Year	912810SQ2	08/15/2040	1.125%	$97.6640
30-Year	912810SP4	08/15/2050	1.375%	$97.6328

On the same day, the following trades were executed:

Issuer	Issue	Price (decimals)
Time Warner Inc.	TWX 6.5 11/15/2036	124.3545
McCormick & Co. Inc.	MKC 4.2 8/15/2047	126.8055
Goldman Sachs Group Inc.	GS 3.25 4/01/2025	110.883
IBM Corp	IBM 7 10/30/2045	156.545
GE Capital International Funding	GE 4.418 11/15/2035	102.9675

Based on the above, assuming that all bonds pay semiannually and that yields are annual yields, complete the following table:

Issue	Yield (%)	Treasury Benchmark	Benchmark Yield (basis-points)	Spread to Benchmark (basis-points)	Yield Ratio
TWX 6.5 11/15/2036
MKC 4.2 8/15/2047
GS 3.25 4/01/2025
IBM 7 10/30/2045
GE 4.418 11/15/2035

2. You observe the yields of the following benchmark securities (all rates are annual):

Year	Yield to Maturity (%)	Spot Rate (%)
1.0	4.3	4.30
2.0	4.7	4.71
3.0	4.9	4.92
4.0	5.2	5.24
5.0	5.5	5.57
6.0	5.7	?
7.0	6	?
8.0	6.5	?
9.0	6.8	7.16
10.00	7.1	7.57

Every security pays a coupon annually, is worth par and has a coupon equal to its yield. Answer the below questions.

(a) Calculate the missing spot rates. (b) What is the price of a 5% six-year security per $100 of face? (c) What is the one-year forward rate starting seven years from now? (d) What is the two-year forward rate starting six years from now?

In your answers, quote the rates as annual rates.