Mortgage Refinance Math
Mortgage Basics
What is a mortgage?
A mortgage is a loan used to buy a home. When you get a mortgage, a lender gives you the money to purchase a property, and in return, you agree to pay back that money, plus interest, over a set period. The house itself acts as collateral for the loan. This means if you fail to make your payments, the lender can take possession of the property. It’s the most common way for people to finance a home purchase without having to pay the full price upfront.
mortgage
noun
A loan agreement where a bank or other financial institution lends money at interest in exchange for taking title of the debtor's property, with the condition that the conveyance of title becomes void upon the payment of the debt.
Principal and interest
Every mortgage payment you make has two main parts: principal and interest. Think of it like a tab at a coffee shop. The principal is the cost of your coffee, while the interest is the fee the shop charges you for letting you pay later.
The principal is the original amount of money you borrowed from the lender. If you get a loan for $300,000, your starting principal is $300,000. Every time you make a payment, a portion of it goes toward reducing this amount.
The interest is the cost of borrowing that money. It’s how the lender makes a profit. Interest is calculated as a percentage of your outstanding principal balance, which is known as the interest rate.
Your monthly payment is a combination of principal and interest, designed to slowly pay down your loan balance over time.
How your loan is paid off
When you first start paying your mortgage, a large portion of your monthly payment goes toward interest. Only a small amount goes to the principal. This is because your principal balance is at its highest, so the interest charged on it is also high.
As you continue making payments, your principal balance slowly shrinks. With each payment, less money is needed for interest, so more of your payment can go toward the principal. Over time, this balance tips. In the final years of your loan, most of your payment will be principal, with very little going to interest.
This process of paying off a loan with scheduled, regular payments is called amortization.
amortization
noun
The process of spreading out a loan into a series of fixed payments over time. Each payment consists of both principal and interest.
Lenders provide an amortization schedule, a table that details exactly how each payment is split between principal and interest over the entire life of the loan. It shows you precisely how your debt decreases with every payment.
Here’s a simplified look at the first few months of an amortization schedule for a $300,000 loan at a 6% interest rate.
| Payment # | Total Payment | Interest Paid | Principal Paid | Remaining Balance |
|---|---|---|---|---|
| 1 | $1,798.65 | $1,500.00 | $298.65 | $299,701.35 |
| 2 | $1,798.65 | $1,498.51 | $300.14 | $299,401.21 |
| 3 | $1,798.65 | $1,497.01 | $301.64 | $299,099.57 |
Notice how the interest portion slowly decreases each month, while the principal portion increases. This gradual shift is the core of how amortization works.
The impact of loan terms
The loan term is the length of time you have to repay the mortgage. Common terms are 15 years and 30 years. The term you choose has a big impact on your monthly payment and the total amount of interest you'll pay.
A 30-year mortgage spreads the payments out over a longer period. This results in a lower, more affordable monthly payment. However, because you're paying interest for a longer time, you'll pay much more in total interest over the life of the loan.
A 15-year mortgage has a higher monthly payment because you're paying the loan off in half the time. The upside is significant: you’ll pay far less in total interest and own your home outright much sooner.
Let's compare a 💲300,000 loan at a 5% interest rate:
- 30-Year Term: Monthly Payment = 💲1,610. Total Interest = 💲279,768
- 15-Year Term: Monthly Payment = 💲2,372. Total Interest = 💲127,025
The shorter term saves over 💲150,000 in interest, but the monthly payment is significantly higher.
Understanding these basic components—principal, interest, amortization, and loan terms—is the foundation for making smart financial decisions about your home. It helps you see not just the monthly cost, but the long-term picture of your loan.
