Answer: To analyze Stephanie's mortgage payments with various additional principal payments, we can use algebraic methods to calculate the remaining balance and total interest paid under different scenarios. Let's consider two scenarios:
Scenario 1: Regular Mortgage Payments without Extra Principal Payments
In this scenario, Stephanie will continue making regular mortgage payments without any additional principal payments. We can calculate the remaining balance and total interest paid using the standard mortgage formula:
Remaining Balance = P * (1 + r)^n - ((1 + r)^n - 1) / r
Total Interest Paid = (Monthly Payment * n) - P
Where:
- P = Principal amount ($300,000)
- r = Monthly interest rate (3.9% / 12)
- n = Total number of payments (30 years * 12 payments per year = 360)
Scenario 2: Mortgage Payments with Extra Principal Payments
In this scenario, Stephanie will make regular mortgage payments and additional principal payments. We will calculate the remaining balance and total interest paid for different amounts of extra principal payments.
Let's consider three different levels of extra principal payments:
- Low Level: An additional $100 per month
- Medium Level: An additional $500 per month
- High Level: An additional $1,000 per month
For each scenario, we can calculate the remaining balance and total interest paid using the same formulas mentioned above, but adjusting the monthly payment by adding the extra principal payment.
To analyze the results, we can create tables or graphs to compare the remaining balance and total interest paid for each scenario.
Please note that the calculations may require a spreadsheet or a mortgage calculator to handle the repetitive calculations involved. If you provide the desired analysis period or any specific details regarding the number of months or years for the analysis, I can provide more specific calculations and visualizations.