# Macaulay duration (MacDur)

I have a question about the weight calculation. For the weights I got

w1 = .0556

w2 = .0514

w3 = .8415

Am I wrong? If so, how do you get the weights from the answer key?

An investor buys a 6% annual payment bond with three years to maturity. The bond has a yield-to-maturity of 8% and is currently priced at 94.845806 per 100 of par. The bond’s Macaulay duration is closest to:

1. 2.62.
2. 2.78.
3. 2.83.

C is correct. The bond’s Macaulay duration is closest to 2.83. Macaulay duration (MacDur) is a weighted average of the times to the receipt of cash flow. The weights are the shares of the full price corresponding to each coupon and principal payment.

Period
Cash Flow
Present Value
Weight
Period × Weight

1
6
5.555556
0.058575
0.058575

2
6
5.144033
0.054236
0.108472

3
106
84.146218
0.887190
2.661570

94.845806
1.000000
2.828617

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I hope this helps.

Period

Cash flow (CF)

Present value (PV)
[CFj/(1+i)N]

Weight
(PVj/PVTotal)

Period × weight

1

6

6 / (1.08)1
= 5.5556

5.5556/94.845806
= 0.0586

1 x 0.0586 = 0.0586

2

6

6 / (1.08)2
= 5.1440

5.1440/94.845806
= 0.0542

2 x 0.0542 = 0.1085

3

106

106 / (1.08)3
= 84.1462

84.1462/94.845806
= 0.8872

3 x 0.8872 = 2.6616

Total

104.0470

94.845806/94.845806 = 1.000

2.8286

Sorry formatting is messed up, not sure how to paste tables in here.