Understanding and Calculating Mortgage Payments
Some people will purchase a home or condo with cash, but the majority of people will apply for a mortgage.
A mortgage is a long-term loan and the property itself is the security. The loan provider decides the minimum down payment (with your input), the payment schedule, the duration of the loan, whether the loan can be assumed by another party, and the penalty for late payments. The title of the home, while under mortgage, belongs to the bank.
mortgage
A mortgage is a type of loan that individuals or businesses take out to purchase real estate. This loan is secured by the property itself, meaning the lender has the right to take possession of the property if the borrower fails to make the required payments.
Mortgage loans are typically paid back over a long period, commonly [latex]15[/latex] or [latex]30[/latex] years, in a series of regular payments that usually cover both the principal (the original amount borrowed) and the interest (the cost of borrowing).
Monthly Mortgage Payments
A mortgage payment is typically made up of four parts: the principal, the interest, taxes, and insurance. This is often abbreviated as PITI.
- Principal: This is the original amount of money you borrowed to buy the house.
- Interest: This is the cost of borrowing money. It’s essentially the profit that goes to the lender.
- Taxes: Property taxes are set by where you live and are typically a percentage of your property’s assessed value. The assessed value is the estimation of the value of your home and does not necessary reflect the purchase or resale value of the home.
- Insurance: This includes both homeowners insurance and, if required, private mortgage insurance.
Private Mortgage Insurance (PMI)
When you purchase a home, you will have to pay a down payment. This means you have money tied to the property, which lenders believe makes you less likely to walk away from a property. The amount of the down payment will be decided between you and the mortgage company.
However, if your down payment is less than [latex]20\%[/latex] of the property value, you will be required to pay private mortgage insurance (PMI). This is insurance you pay for so that the mortgage company is protected if you default on the loan. It often comes to between [latex]0.5\%[/latex] and [latex]2.25\%[/latex] of the original loan amount. It increases your monthly payment. Once you reach [latex]20\%[/latex] of the loan value, you can request that the PMI be dropped. Even if you do not request cancelling the PMI, it will eventually and automatically be dropped.
To manage your mortgage effectively, it’s vital to understand the mechanics of your monthly payments. The calculation involves the Annual Percentage Rate (APR), which serves as the basis for the yearly interest.
mortgage payment formula
The payment, [latex]pmt[/latex], per month to pay down a mortgage with beginning principal [latex]P[/latex] is
where [latex]r[/latex] is the annual interest rate in decimal form and [latex]t[/latex] is the number of years of the payment.
Note, payment to lenders is always rounded up to the next penny.
Mortgage Payment
You can view the transcript for “How To Calculate Your Mortgage Payment” here (opens in new window).
You can view the transcript for “How To Calculate Your Monthly Mortgage Payment Given The Principal, Interest Rate, & Loan Period” here (opens in new window).
You can view the transcript for “How To Calculate A Mortgage Payment Amount – Mortgage Payments Explained With Formula” here (opens in new window).
Understanding the full cost of a loan over its duration is crucial for financial planning. To find the total amount of your payments over the life of the loan, multiply your monthly payments by the number of payments. This can be useful information, but not too many people reach the end of their mortgage since most tend to move before the mortgage is paid off.
total payment formula
The total paid, [latex]T[/latex], on an [latex]t[/latex] year mortgage with monthly payments [latex]pmt[/latex] is [latex]T=pmt\times12\times t[/latex].
To fully grasp the financial implications of a mortgage, it’s essential to understand the concept of financing cost. This cost is the difference between the total amount paid back over the life of the mortgage and the original loan amount, or principal.
cost of financing
The cost of financing a mortgage, [latex]CoF[/latex], is [latex]CoF=T−P[/latex] where [latex]P[/latex] is the mortgage’s starting principal and [latex]T[/latex] is the total paid over the life of the mortgage.
Escrow Payments
We’re aware that mortgage payments consist of four parts, commonly abbreviated as PITI. Our examples so far have focused on the principal and interest. Through an escrow account, the ‘T’ and ‘I’—taxes and insurance—are also collected to ensure these obligations are fulfilled without requiring separate payments.
escrow account
An escrow account is a type of account that your mortgage lender sets up on your behalf when you close on your home. This account is used to pay certain property-related expenses on your behalf. The most common expenses that are paid out of an escrow account are property taxes and homeowners insurance.
Here’s how escrow accounts typically work:
- Escrow Analysis: Each year, your lender performs an escrow analysis to estimate the total cost of your property taxes and insurance for the next [latex]12[/latex] months.
- Monthly Payments: The lender divides the estimated annual cost by [latex]12[/latex] to find a monthly amount, which you pay as part of your monthly mortgage payment.
- Payment of Expenses: When your property taxes and insurance premiums are due, your lender uses the funds in the escrow account to pay these bills on your behalf.
- Adjustments: If the actual expenses turn out to be more or less than estimated, your lender will adjust your monthly payment at the next escrow analysis.
APR, or Annual Percentage Rate, represents the yearly interest rate charged on a loan, including any fees or additional costs associated with the transaction.