Assignment X1 Q1.12

[sophieactrainee]

Hi there,

I do not understand the logic in ii).

We have calculated the equivalent constant force of interest per annum for period t=0 to t=10, lets say it is delta. This was calculated in part i)

Why can we not then go ahead and calculate in ii), the accumulated value at time 7 of an investment of 250 at time 0, as 250*exp(delta*7) ?

Similarly, why can't we calculate accumulated value of an investment of 150 at time 5, valued at time 7 as 150 A(0,7)/A(0,5) = 150 exp(-delta*5)*exp(delta*7) ?

In the solution, it wants us to instead calculate the accumulated value at time 7 of an investment of 250 at time 0 as: 250 exp( int(0,7) 0.03 - 0.005s + 0.001s^2 ) ? Why aren't we allowed to use the constant equivalent force of interest?

Could someone explain this please?

Much appreciated

 

[James Nunn]

Hi Sophie

As you say, part (i) was to calculate an equivalent constant delta for the period 0 to 10. This delta can be thought of as the average of deltas over the period 0 to 10, and so can only be used to discount all the way from time 10 to time zero or to accumulate all the way from time 0 to time 10. That's because the real delta varies and so this constant delta will not be correct (ie equivalent to the real variable delta) for other periods - there would be different equivalent constant delta (as we would be averaging a different set of varying deltas over a different period).

Hopefully that helps. All the best with your studying.

 

[sophieactrainee]

Thank you