Question

What is the Macaulay Duration of a 6.8% annual coupon bond with 3 years to maturity, $1,000 face value, and yield to maturity of 6.8%? Round to three decimal places.

Answer 1

No of periods = 3 years

Cashflow = Coupon rate * Face value

Cashflow = 6.8% * $1000

Cashflow = $68

For time period 1

Discount factor = 1 / (1 + Yield to Maturity)^{Time period}

Discount factor = 1 / (1 + 6.8%)¹

Discount factor = 0.9363

Present value of Cashflow = Cashflow * Dicount factor

Present value of Cashflow = $68 * 0.9363

Present value of Cashflow = $63.67

Weight = Present value of Cashflow / Total(Present value of Cashflow)

Weight = $63.67 / $1000

Weight = 6.37%

Weighted average of Time = Weight * Time period

Weighted average of Time = 6.37% * 1

Weighted average of Time = 0.0637

Time period	Yield to Maturity	Discount Factor	Cashflow	Present value of Cashflow	Weight	Weighted average of Time
1	6.8%	0.9363	$68	$63.67	6.37%	0.0637
2	6.8%	0.8767	$68	$59.62	5.96%	0.1192
3	6.8%	0.8209	$1,068	$876.71	87.67%	2.6301
		Total	$1,204	$1,000.00	100.00%	2.8130

Macaulay Duration = 2.8130 years