Question

Consider an annuity contract that pays out $45 at the end of each of the next four 6-month intervals (payments are to be made 6, 12, 18, and 24 months from today). What is this annuity's Macaulay duration (in years)? Assume this contract is currently trading at a yield of 6%.

Round your answer to 3 decimal places. For example if your answer is 5.5175, then please write down 5.518.

Hint: First price this contract, and then calculate its duration accordingly.

Answer 1

Period	Cash Flow from Bond	Discounting factor = 1/(1+R)^N	PV of the cash flows = Cash flow x Df	Weighted cash flow = Period x Cash flow	Present value of weighted cash flow = Weighted Cash flow x Df
N	CF	Df = 1/(1+6%/2)^N	PV = CF x Df	WCF = CF x N	WPV = WCF x Df
1.00	45.0000	0.9709	43.6893	45.0000	43.6893
2.00	45.0000	0.9426	42.4168	90.0000	84.8336
3.00	45.0000	0.9151	41.1814	135.0000	123.5441
4.00	45.0000	0.8885	39.9819	180.0000	159.9277
		Total = P = Current Price =	167.2694	Total = Weighted Price = WP	411.9947

Macaulay Duration = 0.5 x WP/P = 0.5 x 411.9947 / 167.2694

Macaulay Duration = 1.232 Years