Decreasing perpetuity problem A perpetuity pays 1000 immediately. The second payment is 97% of the first payment and is made at the end of the fourth year. Each subsequent payment is 97% of the previous payment and is paid four years after the previous payment. Calculate the present value of this annuity at an annual effective rate of 8%.
My attempt:
Let X denote the present value.
$x/(1+i) + 0.97x/(1+i)^5 + 0.97^2x/(1+i)^9 + ...$ = 1000
where $i = 0.08$, however I am not sure how to solve this or if this is correct

This is a perpetuity due decreasing in geometric progression and payable less frequently than interest is convertible.
The effective interest rate per period is 
$$
i=(1+0.08)^4-1=36.05\%
$$
and the growing rate is $g=-3\%$ (decreasing).
So the perpetuity due has the present value
$$
PV=1000\frac{1+i}{i-g}=3,484.07
$$
