FRA Value Discounting

Hi,

I am referring to CFAI Volume 5 Reading 40 (page 293 in the ebook version) - the paragraphs between Exhibit 10 and Example 8.

The text mentions that to derive the value of the original FRA contract at a time g after initiation, you need to discount the difference between the cash flows at time h + m of the original FRA contract and a new FRA contract and bring it back to present value at time g. The text states that “discounting will be over the period h + m - g”. This makes sense, I agree with all of this.

However, when they calculated the value of the existing FRA contract at day g, they discounted the net cash flow (this cash flow was shown in Exhibit 10) at time h + m of 0.00025 back using the 60 day rate of 3% on day g (the calculation of which was shown a few paragraphs after Exhibit 10 and just before Example 8).

My question is: doesn’t discounting the h + m cash flows using the 60 day rate at g only discount the cash flow back h - g periods, ignoring the 90 days between h and m? From how I see it, the cash flow was only discounted back h-g periods, not the full h + m - g periods.

I hope this post wasn’t too convoluted. If you have a question about where exactly in the book I’m referring to, please ask - I tried my best to clearly point out the relevant section.

Can someone explain this?