Question

1. A bond issued by the town of Brockton has a 3% yield to maturity and a coupon rate of 4%. The bond has 4 years to maturity and pays coupons semi-annually. What is the bond's current price?

2. A credit card has an annual rate of 18% with monthly compounding. What is the EAR?

3. A bond issued by UMass Boston currently sells for $1000. It has 10 years to maturity and a yield to maturity of 2%. The bond pays coupons semi-annually.

a) What is the bond's coupon payment?

b) What is bond's coupon rate?

Answer 1

	Question No:-1		details as given in question		Since the coupon is paid semi annual the YTM, Coupon rate and no of period is divided by 2
			Yield to maturity (YTM)	3%	1.50%
			Coupon rate	4%	2%
			No of year	4	8
			Coupon duration	Semi- annually
			What is bonds current price
			Computation of price of the bond
		Year	Cash flow(i.e. coupon payment and principle payment of bond	Present value factor @1.5%	Present value of cash flow
		A	B	C	D=B*C
		1	2	=2/(1+1.5%)^1	1.97
		2	2	=2/(1+1.5%)^2	1.94
		3	2	=2/(1+1.5%)^3	1.91
		4	2	=2/(1+1.5%)^4	1.88
		5	2	=2/(1+1.5%)^5	1.86
		6	2	=2/(1+1.5%)^6	1.83
		7	2	=2/(1+1.5%)^7	1.80
		8	102	=102/(1+1.5%)^8	90.55
				Price of the Bond	103.74
	Question No:-2
		r	Rate of interest
		m	no of months in year
			Effective annual rate=	(1+r/m)^m-1
			Effective annual rate=	(1+18%/12)^12-1
			Effective annual rate=	(1.015)^12-1
			Effective annual rate=	=1.19561817146153-1
			Effective annual rate=	0.19562
			Effective annual rate=	i.e. 19.56%
	Question No:-3		As per the bond theorem when the market value of bond is equal to the face value of the bond then Yield to maturity and coupon rate of the bond will be same
			So the in the based on the above the explanation coupon payment will 1% of market value of bond as the coupon is semi annually paid the coupon rate will be divided by 2
				Semi -annually	Annually
			Coupon payment are=	1,000*1%	1,000*1%
			Coupon payment are=	10	20
			Coupon rate=	=2%/2
			Coupon rate=	1%	2%