How can you determine principal and interest rate of a loan given the term, monthly payment and first period interest? I did it the hard way by tabulating interest payments for a range of interest rates and principals then calculating principal for specific combinations.

For a 60 month loan with a monthly payment of $594.40 and first month interest component of $124.26, I got a principal of $31,700 and an interest rate of 4.75%. How can I confirm this is a unique solution through $50,000 and 15% other than increasing resolution in the table? Is there a solution I'm missing in the 7-8% range?

Thanks,
Sixto
87 300D