Schweser Mock Volume 2 Exam 3 Q 56 difference, discount, original

whew1110

Sorry this question is too long to write out, but basically we have an FRA and we are asked to find the FRA value 3 months into the deal. According to the CFAI texts, we are supposed to use the formula given on page 27 (CFAI Volume 6) by
1/(1+L(h-g) - (1+FRA)/(1+L(h+m-g))
but in the solution they do it totally differently, they recalculate the FRA rate, find the diff between it and the original rate and discount it….why the huge difference between the methods?
Thanks in advance.