I've seen [this answer](https://math.stackexchange.com/questions/993052/using-ia-overline-n-rceil-i-from-exam-fm) and I understand the methodology, but I am wondering why my original solution using a different method did not work.

This is the sample problem in my study guide for Exam FM:

> 
> Olga buys a 5-year increasing annuity for X. Olga will receive 2 at the end of the first month, 4 at the end of the second month, and for each month thereafter the payment increases by 2. The nominal interest rate is 9% convertible quarterly. Calculate X.
> 
> 
> 

$X$ is clearly the present value of this increasing annuity.

My study guide lists a formula for $(I^{(m)}a)^{(m)}\_{\bar{n}|}$ as $$\frac{\ddot{a}^{(m)}\_{\bar{n}|}-nv^n}{i^{(m)}}$$ This is supposed to be the present value of payments $\frac{1}{m^2}, \frac{2}{m^2}, \frac{3}{m^2},...,\frac{mn}{m^2}$ made at times $\frac{1}{m}, \frac{2}{m}, \frac{3}{m}, n$ respectively.

I initially thought the present value would be given by $288(I^{(12)}a)^{(12)}\_{\bar{5}|}$ - this would give payments every month of $\frac{288}{144}=2, \frac{288\*2}{144}=4, ...$. Applying the formula, however, gives me an answer that is far too large.
$$i \approx 9.3083\%$$
$$i^{(12)}\approx8.9333\%$$
$$\ddot{a}^{(12)}\_{\bar{5}|} = \ddot{a}\_{\bar{60}|0.7444\%} \approx 48.6083$$
$$288(I^{(12)}a)^{(12)}\_{\bar{5}|} = 288\frac{48.6083-5(1.093083^{-5})}{0.08933} = 288(508.2575)=146378.16$$
The actual answer is $\approx 2729$.

Is this payment stream not accurately described using $(I^{(m)}a)^{(m)}\_{\bar{n}|}$? If so why not? Admittedly, this is an overly-complex way to solve the problem compared to the linked answer but I'm hoping to better understand this type of increasing annuity.