Question

The force interest is given by

(t)={0.08 - 0.001t ,0<t<3

0.025t-0.04,3<t</5

0.03, t>5

Calculate the present value at time 2 of a payment £1000 at time 10

Answer 1

First lets see what force of interest is.

0.08 − 0.001t, when 0 ≤ t < 3

0.025t − 0.04, when 3 ≤ t < 5

0.03, when t ≥5

Using this and the above formula for present value, we get

Present Value of a payment at time 2 of 1000000 at time 10 is

1000000*exp( -[0.2355 - 0.158])*exp ( -[0.1125 + 0.0075])*exp ( -[0.3 - 0.15])

= 1000000*exp(-0.3475) = 706,452.

Lets say that the annual effective rate of interest is i , then

706452(1 + i)⁸ = 1000000

⇒ i = 4.44%