Final answer:
The principal balance at the end of the first month will depend on the monthly payment amount which is not provided. Normally, mortgage payments are primarily interest initially, with a smaller portion reducing the principal.
Step-by-step explanation:
To determine Johnny's principal balance at the end of the first month after taking out a $500,000, 30-year mortgage with an APR of 4.15% and making an extra payment of $1,000, we need to calculate the monthly payment and subtract it along with the extra payment from the initial principal. Unfortunately, with the provided data, we do not have the exact monthly payment amount, which is essential to calculate the current balance. Normally, we would use a mortgage calculator or the appropriate financial formulas to find the monthly payment and proceed with the calculation. However, we can note that with mortgages, the initial payments are mostly interest, so the principal reduction in the first month would be less significant.