An annuity immediate has $40$ initial quarterly payments of $20$ followed by perpetuity of quarterly payments of $25$ starting in the eleventh year. Find the present value at $4\% $ convertible quarterly.
My answer comes as $2322.722733$, but the book answer is $2335.83$. I just want to verify.
The interest accrued per quarter is $i^{(4)}/4 = 0.01$. So the present value is $$20 a_{\overline{40}|0.01} + 25 v^{40} a_{\overline{\infty}|0.01} = 20 \frac{1 - (1.01)^{-40}}{0.01} + 25(1.01)^{-40} \cdot \frac{1}{0.01} = 2335.83.$$ The book's answer is correct.
Alternatively, you can regard the cash flow as being a perpetuity of $20$ at $1\%$, plus a perpetuity of $5$ at $1\%$ deferred until the $41^{\rm st}$ payment: $$PV = (20 + 5 v^{40}) a_{\overline{\infty}|0.01} = (20+5(1.01)^{-40})(100) = 2335.83.$$
If you share your calculation, I may be able to point out where you made an error.