Answer:
1.9516 years.
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.