In section 3.1 how does I (p)/P becomes amount for each interest payment and how does the accumulated value at each time becomes equal to I? I don't understand the first equation derived .
If i(p) is the nominal rate of interest payable pthly, then i(p)/p shall be effective rate of interest for the pth period. Accordingly, i(p)/p becomes the amount of each interest payment. Refer to page 2 of the chapter, last paragraph, starting with 'Essentially'. It might clarify the idea. Regards, Shyam
I, myself am getting a bit confused on the equation as to why (1+i)^[(p-1)/p] (and hence further ones) has been multiplied to each term. I guess it has been done so because the statement above it states that the accumulated value of the interest payments at time 1 would be...so and so.... The accumulated value of the p interest payments, each of amount i(p)/p , is equal to i. (i being the annual effective ROI, and i(p)/p being the nominal ROI payable pthly) Then, the resulting series on the LHS is a geometric progression (hope you understand it), which has been summed using the GP summation formula, a*(1-r^n)/(1-r), if r< or = 1; where a is the first term, r is the common multiple and n is the number of terms. Solving further, we finally get the formula for arriving at nominal rate of interest, if effective rate of interest is given. Hope this helps! Regards, Shyam
I understood the calculations after that i am only having a hard time understanding how that equation is formed in the first place. Are derivations asked in CT 1 exam ?
They're just accumulating all the interest payments until the end of the year so we can compare it with an annual rate. For the IFoA derivations are asked - but have been limited to Chapter 7, 14 and 15.
