Question

You are given

(i)?(?)=??2+??+?

(ii)?(0)=100

(iii)?(1)=110

(iv)?(2)=136

Determine the force of interest at time ?=2.

Answer 1

A(0) = B*0*0 + C*0 +D

A(0) = D = 100

Hence D=100

A(1) = B*1*1 + C*1 +D

110 = B+C+100

B+C = 10 -------------------equation 1

A(2) = B*2*2 + C*2 +D

136=4B+2C+100

2*(2B+C) = 36 ------------------equation 2

From equation 1 and 2, we get

2*(B+10) = 36

B = 8

From equation 1, C =2

Force of interest at time t =

where is the first derivative of the function

Force of interest at time t = (2*B*t +C) / (B*t*t + C*t +D)

Substituting t=2, we get

Force of interest at time 2 = (2*8*2+2) /136

Force of interest at time 2 = 0.25