CT1 IFoA April 2010 Q1 (ii)

[9346776]

Why is it the dividend of £2.80 was forwarded to the 3rd month before first discounting it to t=0 so that we can subtract with 60 first before accumulating. I first discounted it and my answer is 58.53008239 and the exam answer is 58.09 without discounting first

 

[Mark Mitchell]

The formula to use here is the standard formula (S0 - I)*e^(delta*T).

Here:
S0 = 60
I = present value of the income = 2.8*e^(-0.06*2/12)
e^(delta*T) = e^(0.06*3/12)

This gives:

(60 - 2.8*e^(-0.06*2/12))*e^(0.06*3/12) = 60*e^(0.06*3/12) - 2.8*e^(0.06*1/12))

as the accumulation and discounting partially cancel out.