• We are pleased to announce that the winner of our Feedback Prize Draw for the Winter 2024-25 session and winning £150 of gift vouchers is Zhao Liang Tay. Congratulations to Zhao Liang. If you fancy winning £150 worth of gift vouchers (from a major UK store) for the Summer 2025 exam sitting for just a few minutes of your time throughout the session, please see our website at https://www.acted.co.uk/further-info.html?pat=feedback#feedback-prize for more information on how you can make sure your name is included in the draw at the end of the session.
  • Please be advised that the SP1, SP5 and SP7 X1 deadline is the 14th July and not the 17th June as first stated. Please accept out apologies for any confusion caused.

CT1 Ch15 Q15.2

S

saksham

Member
I am not at all able to understand q 15.3 pg 6. Anyone please explain
 
We have \(i_k, \quad k\in \{0,1,\ldots n\}\) i.i.d rvs with

\( p(i_k = a) =\begin{cases} \frac{1}{3} & \text{ for } a\in \{0.02,0.04,0.06\} \\0 \text{otherwise} \end{cases}\)

and \(S_n = \prod_{k=1}^{n} (1+i_k)\)

We have been asked to find \( \Pr(S_n = 1.02\times 1.04^{n-1})\)

Since \(S_n\) can take \(3^n\) values with each value being equally likely and there are \(\binom{n}{1}\) possibilities where for one of the year interest rate is \(0.2\) and for \(n-1\) years it is \(0.04\)

therefore \(\Pr(S_n = 1.02\times 1.04^{n-1}) = \dfrac{n}{3^n}\)
 
Back
Top