Question

The force of interest is given by:

𝛿(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 of £1,000 at time 10.

Answer 1

$=100exp[(0.08) 8+(0.02) ln\frac {1 1}{2}]$

$=1000e^{-0.04}3.67^{-0.02}$

$=£706.45$