Question

Julia Chen just purchased a $1,000 face value bond for $987. The bond pays $50 in interest every six months and matures in five years. The yield to maturity for this bond is __________ percent. (Note: This question requires a financial calculator.)

		10.6
		10.2
		10.0
		10.3

Answer 1

Using the financial calculator we can calculate the rate as follows:

• FV = 1000
• PV = -987
• N= 5 x 2 = 10 as the interest payment is semi annual
• PMT = 50
• CPT I/Y = 5.169, however this is the semi annual yield, we need to annualize it therefore we need to multiply it by 2 and therefore the YTM is 5.169 x 2 = 10.34%
• PV is input as a negative number because that is the price we need to pay to purchase the bond

The same can be calculated by the following formula in Excel =RATE(10,50,-987,1000) this will give rate = 5.169 and then we need to multiply it by 2 to get 10.34% or 10.3 as suggested by the last option or the annualized YTM

following schedule verifies the same:

Year	CF	Discount Factor	Discounted CF
0	$                      -	1/(1+0.05169)^0=	1	1*0=	-
1	$               50.00	1/(1+0.05169)^1=	0.950850536	0.950850535804277*50=	47.54
2	$               50.00	1/(1+0.05169)^2=	0.904116741	0.90411674143928*50=	45.21
3	$               50.00	1/(1+0.05169)^3=	0.859679888	0.859679888027157*50=	42.98
4	$               50.00	1/(1+0.05169)^4=	0.817427082	0.817427082150783*50=	40.87
5	$               50.00	1/(1+0.05169)^5=	0.777250979	0.777250979043998*50=	38.86
6	$               50.00	1/(1+0.05169)^6=	0.73904951	0.739049509878385*50=	36.95
7	$               50.00	1/(1+0.05169)^7=	0.702725622	0.70272562245375*50=	35.14
8	$               50.00	1/(1+0.05169)^8=	0.668187035	0.668187034633542*50=	33.41
9	$               50.00	1/(1+0.05169)^9=	0.635346	0.635345999898775*50=	31.77
10	$               50.00	1/(1+0.05169)^10=	0.604119084	0.604119084424854*50=	30.21
10	$         1,000.00	1/(1+0.05169)^10=	0.604119084	0.604119084424854*1000=	604.12
				Price = Sum of all Discounted CF	987.00