sophieactrainee
Keen member
Hi ( I hope this is okay to bombard the forum with multiple questions!!) 
Please could you help with why my logic is wrong here, for question 5 ii) a):
My solution:
We want to find the expected value and standard deviation at the end of year 15 for Option A
Sum of 500 invested for each policyholder in fund
Expected annual effective rate of interest 3.5%
S.d of annual returns 2%
Annual rates of return independent and (1+i_t) ~ logN(mu,sigma^2)
Where i_t is rate of return in year t
Policyholder receive accumulated investment at end of 15 years
Expected value
E[500*(1+i_1)(1+i_2)..(1+i_15)] = 500* E[1+i_1] * E[1+i_2] * E[1+i_3] *.. E[1+i_15] = 500*15*1.035=7762.5 - why is this wrong? I get this is far too large an answer so it would ring alarm bells.. but I can't see how it's wrong? I have used the following reasons:
E[(1+i_t)] = 1.035, and each i_t is independent?
Please could you help with why my logic is wrong here, for question 5 ii) a):
My solution:
We want to find the expected value and standard deviation at the end of year 15 for Option A
Sum of 500 invested for each policyholder in fund
Expected annual effective rate of interest 3.5%
S.d of annual returns 2%
Annual rates of return independent and (1+i_t) ~ logN(mu,sigma^2)
Where i_t is rate of return in year t
Policyholder receive accumulated investment at end of 15 years
Expected value
E[500*(1+i_1)(1+i_2)..(1+i_15)] = 500* E[1+i_1] * E[1+i_2] * E[1+i_3] *.. E[1+i_15] = 500*15*1.035=7762.5 - why is this wrong? I get this is far too large an answer so it would ring alarm bells.. but I can't see how it's wrong? I have used the following reasons:
E[(1+i_t)] = 1.035, and each i_t is independent?