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Prospective and Retrospective Methods Question
Hello, I was looking at Example 37.2 from "A Basic Course in the Theory of Interest and Derivatives Markets: A Preparation for the Actuarial Exam FM/2" by Marcel B. Finan and I am confused why they set it up like this:
The problem reads: A loan is being repaid with 16 quarterly payments, where the first 8 payments are each $200 and the last 8 payments are each $400. If the nominal rate of interest convertible quarterly is 10%, use both the prospective method and the retrospective method to find the outstanding loan balance immediately after the first six payments are made. Using the prospective method, it was set up like this: B(p,6) = 200(v + v^2) + 400(v + v^2 + ....+ v^8) If the question asks for the loan balance after 6th payment shouldn't it be: 200 * (annuityimmediate of n = 10) and not include the 400. If someone can clarify this, that would be helpful. 
#2




Since on the time diagram, we are at time 6. If you wrote 200 * (annuity immediate with n=10), then you are saying that starting at time 8, only payments of 200 are made. But in reality, at time 68, it's still 200, but starting with time 9, payments are 400 each rather than just 200. So 200(v + v^2) accounts for time 6 to 8 and then 400(v + v^2 + ....+ v^8) starting at time 9. Hope that helps!
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