A pension fund must pay out $1 million next year,$2 million the following year and then $3 million the year after that.If the discount rate is 8% what is the duration of this set of payments?

Question

Quizplus · Accepted Answer

The duration of the set of payments can be calculated using the formula:
Duration = [(Present value of cash flows weighted by time) / Total present value of cash flows]
Using a financial calculator or spreadsheet, the present value of each cash flow can be calculated as follows:
PV of $1 million = $925,926.00
PV of $2 million = $1,735,053.16
PV of $3 million = $2,367,355.71
Total present value of cash flows = $4,028,334.87
Weighted present value of cash flows = ($925,926*1 + $1,735,053.16*2 + $2,367,355.71*3) = $11,735,000.10
Duration = $11,735,000.10 / $4,028,334.87 = 2.29 years (rounded to two decimal places)

A Pension Fund Must Pay Out $1 Million Next Year,$2