Investment Property Perpetual IRR Considering Loan Repayments

Hi
I need to calculate the IRR of a real estate investment which generates rent in perpetuity.
The initial rental income is $2173.91 per month, compounding at 0.2% per month
The initial deposit is $108,695.65
The monthly repayments are $1,738.85 for 25 years.
I understand the IRR is the discount rate which sets the NPV to 0. So i mucked around in Excel, plotted out cashflows to some huge arbitrary value and found the IRR to make the NPV = 0 for this essentially infinite cash flow stream is 0.998%.
What i would like to know is how can i prove this numerically. Is it possible, because the cash flows are not ‘trendable”. After the 25 year mark, once the loan is paid off, discounted cashflow increases significantly. Even with the IRR discount factor applied, there is still a significant jump in the discounted cash flow after the loan is paid off.
Any help appreciated. Thanks