Question

James has a loan of 10,000, which is to be repaid with 10 level annual payments at an annual effective interest rate of 14.5%.

Calculate the Macaulay duration of the loan using the 14.5% interest rate.

Answer 1

		Caclualtion of annual payment	annual payment
		=PMT(14.5%,10,-10000,0,0)	1,954.69
Years (T)	Cash flow	Present value calculation	Present value (PV)	Duration D = (PV*T)
1	1,954.69	1954.69/(1+14.5%)^1	1,707.15	1,707.15
2	1,954.69	1954.69/(1+14.5%)^2	1,490.96	2,981.93
3	1,954.69	1954.69/(1+14.5%)^3	1,302.15	3,906.45
4	1,954.69	1954.69/(1+14.5%)^4	1,137.25	4,549.00
5	1,954.69	1954.69/(1+14.5%)^5	993.23	4,966.16
6	1,954.69	1954.69/(1+14.5%)^6	867.45	5,204.71
7	1,954.69	1954.69/(1+14.5%)^7	757.60	5,303.19
8	1,954.69	1954.69/(1+14.5%)^8	661.66	5,293.27
9	1,954.69	1954.69/(1+14.5%)^9	577.87	5,200.81
10	1,954.69	1954.69/(1+14.5%)^10	504.69	5,046.88
Total	10000.00	44159.55
		90
Macaulay Duration = Duration D / Present value of cashflows	Macaulay Duration = 44159.55 / 10000 = 4.42