Mortgage guides
Chapter 3: How your monthly principal-and-interest payment budget determines your loan amount | For curious minds
Sources and calculations checked:
Use the monthly principal-and-interest payment budget from chapter two, then reverse chapter one's principal-and-interest payment formula to estimate a loan amount.
Terminology guide: check the meanings used in these articles
Chapter two calculated your monthly principal-and-interest payment budget. Now we work backward: how much loan can that budget support?
Just want the takeaway?
The loan amount you can afford depends on your monthly principal-and-interest payment budget, the interest rate, and the loan term.
The formula shows how these factors determine the loan amount. For an estimate based on your situation, talk to me about your budget. You do not need to follow the math to get started.
Assumptions behind the formula
A fixed-rate, fully amortizing loan, with end-of-month, on-time payments and no extra principal payments. The formula describes a mathematical repayment arrangement, not loan approval.
This chapter solves for a loan amount using principal and interest only. The CFPB’s payment breakdown distinguishes principal and interest from property taxes, homeowners insurance, and applicable mortgage insurance. Chapter two already subtracts these other costs and applicable HOA fees from total housing expenses.
Step 1: Reverse chapter one’s formula
Chapter one gave us the monthly principal-and-interest payment formula:
Rearranging this equation to solve for the loan amount P gives:
Only four symbols are needed here:
- P is the loan amount we want to calculate.
- M is the monthly principal-and-interest payment budget calculated in chapter two.
- r is the contractual annual rate, written as a decimal, divided by 12.
- n is the total number of monthly payments over the loan term.
The formula rearranges chapter one’s payment equation; it is not an approval rule. Fannie Mae’s debt ratio guidance describes income and debt requirements for its programs; requirements vary by program.