Question

e) 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

$= 1000 exp[(-0.08) 8 + (0.02) ln 11/3]$

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

$= £706.45$