Calculating interest rate with changing payments and baloon payments

For varying payments, the interest rate is the IRR of the cash flows. Note that for Excel, these must be signed cash flows. This can be confirmed with an amortization schedule demonstrated below.

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Note that E2 and E3 (interest rates) are rounded for display purposes. Their actual values are 1.98346981427899% and 23.8016377713479%.

Also note that in some regions, the annualized interest rate might be calculated differently.

Finally, note that in some regions, the actual annual interest rate might not be the same as the stated annual percentage rate (APR) due to regulatory differences in calculation.

PS.... It is interesting to note (no pun intended) that some monthly payments are not sufficient to cover the monthly interest, resulting in "negative amortization"; that is, a negative principal payment and an increase in the loan balance.