Question

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?

Answer 1

Answer: 2.29 years

Explanation:

First find the present value of the payments.

= (1,000,000 / 1.08) + (2,000,000/1.08^2) + (3,000,000/1.08^3)

= 925,925.9259 + 1,714,677.6406 + 2,381,496.72306

= $5,022,100.28956‬

Duration = ∑Proportion of payment

= (925,925.9259/5,022,100.28956) + (1,714,677.6406/ 5,022,100.28956‬ ) + (2,381,496.72306 / 5,022,100.28956‬ )

= 2.28983

= 2.29 years