Question

A fund will need to pay out $2 million next year, $3 million the following year, and then $5 million in the fifth year. If the discount rate is 6%, what is the Macaulay duration of this set of payments?

A. 3.05

B. 3.12

C. 2.85

D. 3.50

Answer 1

Given about a fund,

Payment in year 1 = $2 million

Payment in year 2 = $3 million

Payment in year 5 = $5 million

discount rate d = 6%

Duration is calculated as below table:

PV of payment = payment/(1+d)^year

Total PV = sum of all PV = $8.29 million

weight = PV of payment/ price

duration of each coupon = period*weight

duration of the bond = sum of all duration = 3.12 years

Year	payment	PV of Cash flow=Payment/(1+d)^year	weight = PV of Payment/Price	Duration = weight*year
1	$                  2.00	$                  1.89	0.2275	0.2275
2	$                  3.00	$                  2.67	0.3220	0.6439
3	$                       -	$                       -	0.0000	0.0000
4	$                       -	$                       -	0.0000	0.0000
5	$                  5.00	$                  3.74	0.4505	2.2527
	Total PV	$                  8.29	Duration	3.12

Option B is correct.