I am trying to solve the following problem
Olga buys a 5-yr 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 $X$.
Below is my attempt. I did not use the formula for the special case where P=Q=1 but I chose to use the general formula. But I got the different answer and I don't which step had the problem
$j = \left(1+\tfrac{.09}{4}\right)^{1/3}-1 \approx 0.007444$.
$X = Pa_{\overline {n} \rceil j}+Q*\frac{a_{\overline {n} \rceil j}-nv^{n}}{j}$
$X = (P+\frac{Q}{j})a_{\overline {n} \rceil j}-Q\frac{nv^{n}}{j}$, using the TVM calculator
I got $X = 13068.1656-10304.2044=2763.9612$, which is close to answer C: 2780 But the correct answer is B: 2730
$P=Q=2\\ j\approx.007444\\ a_{\bar{n}|j}=\frac{1-1.007444^{-60}}{.007444}\approx48.25\\ nv^n=60\times1.007444^{-60}\approx38.45\\ X=\color{blue}{(2+2\div.007444)\times48.25}-\color{green}{2\times38.45\div.007444}\\ \approx\color{blue}{13060}-\color{green}{10330}=2730$