Question

A pension plan is obligated to make disbursements of $1.8 million, $2.8 million, and $1.8 million at the end of each of the next three years, respectively. Find the duration of the plan's obligations if the interest rate is 9% annually.

Answer 1

1.9516 years.

Step-by-step explanation:

So, the best and fastest way to solve this question is to use excel. So the first step is to calculate the Present Value of Cash Flow for the three cash flows and sum them up.

(A).

(1). For cash flow = $1,800,000, time = 1.

Present Value of Cash Flow:

$1,800,000 / (1 + 9%)^1

= 1651376.14678899082.

(2). For cash flow = $2,800,000, time = 2.

= $2,800,00/ (1 + 9%)^2.

= 2356703.98114636815.

(3). For cash flow = $2,800,000, time = 3.

= $1,800,000 / (1 + 9%)^3.

= 1389930.26410991568.

Thus, 1651376.14678899082 + 2356703.98114636815 + 1389930.26410991568.

= 5398010.39204527465.

(B). Also, 1651376.14678899082 ×( time = 1) = 1651376.14678899082.

2356703.98114636815 × (time= 2 ) = 4,713,407.9622927363.

1389930.26410991568 × (time = 3) = 4169790.79232974704.

Thus, 4169790.79232974704 + 1651376.14678899082 + 4,713,407.9622927363.

= 10534574.90141147416.

Hence, duration = 10534574.90141147416/ 5398010.39204527465.

= 1.95156625058292731

Approximately 1.9516 years.