Question

1) Semiannual compounding and/or that all coupon bonds are semiannual-pay bonds;

2) Bonds are $1000 par.

What is the Macaulay duration of a semiannual-pay 8.16 percent coupon bond with 7 years to maturity and a yield to maturity of 7.52 percent? Answer to two decimals, carry intermediate calcs. to four decimals.

****Please show the steps of calculation and the inputs of financial calculator

Answer 1

Time	Cashflow	[email protected]%	Present Value (Cashflow*PVF)	Weight based on present value	Time*Weight
1	40.8	0.964	39.32	0.0380	0.04
2	40.8	0.929	37.90	0.0366	0.07
3	40.8	0.895	36.52	0.0353	0.11
4	40.8	0.863	35.20	0.0340	0.14
5	40.8	0.831	33.92	0.0328	0.16
6	40.8	0.801	32.69	0.0316	0.19
7	40.8	0.772	31.51	0.0305	0.21
8	40.8	0.744	30.37	0.0294	0.23
9	40.8	0.717	29.27	0.0283	0.25
10	40.8	0.691	28.21	0.0273	0.27
11	40.8	0.666	27.19	0.0263	0.29
12	40.8	0.642	26.20	0.0253	0.30
13	40.8	0.619	25.25	0.0244	0.32
14	1040.8	0.596	620.79	0.6002	8.40

Duration for semi annual bond = Time*Weight /2

= 11/2

= 5.50 years

Note : Since the bond makes semiannual interest payments, total no. of period is 14 (7*2), cashflow per period is 40.80(1000*8.16%/2) and cashflows are discounted at 3.76% (7.52/2).