The problem is :
Given a discount rate of $5\%$ compounded quarterly, what’s the PV of an annuity-due with annual payment $1,300$ for $5$ years?
It's annuity due so $a\ double\ dot\ n$. $1300 \ a \ double \ dot \ 5$
Following the formula, I would do $\frac{1-(\frac{.05}{4})^{20}}{\frac{\frac{.05}{4}}{1+\frac{.05}{4}}}$ since the denominator is $d=\frac{i}{i+1}$
This is nowhere near the answer provided. Intuition and correct set up is appreciated
Let be $p=1300$ the annual payment for $n=5$ years and $d^{(4)}=5\%$ discount rate compounded quarterly. So $1-d=\left(1-\frac{d^{(4)}}{4}\right)^4=\frac1{1+i}$ and the annual effective discount rate is $d=4.91\%$ and the annual effective interest rate is $i=5.16\%$. The present value of the annuity due is $$ PV=p\times \ddot a_{\overline{n}|i}=p\times (1+i)a_{\overline{n}|i}=p\times (1+i)\frac{1-(1+i)^{-5}}{i} $$ Observing that $\frac{1+i}{i}=\frac{1}{d}$ $$ PV=p\times \frac{1-(1-d)^{5}}{d}=p\times 4\,\frac{1-\left(1-\frac{d^{(4)}}{4}\right)^{20}}{d^{(4)}}=5,892.28 $$
You can also evaluate directly from $$ \begin{align} PV&=p+p (1-d)+p(1-d)^2+p (1-d)^3+p(1-d)^4\\ &=p+p \left(1-\frac{d^{(4)}}{4}\right)^4+p\left(1-\frac{d^{(4)}}{4}\right)^{8}+p \left(1-\frac{d^{(4)}}{4}\right)^{12}+p\left(1-\frac{d^{(4)}}{4}\right)^{16} \end{align} $$