# Mortgage Calculator

Created by Davide Borchia
Last updated: Jul 03, 2022

Buying property is not easy: learn everything you need to know about a home loan with our mortgage calculator.

Our mortgage loan calculator will tell you:

• What is a mortgage;
• What are the simple elements of a mortgage;
• Additional elements of a mortgage;
• The mortgage formula;
• An example of how to use our home loan calculator.

For similar tools, check our loan calculator or our velocity of money calculator.

## What is a mortgage?

A mortgage is a loan that allows you to purchase a property. Since real estate usually has a high value, it's not common to afford a house "on the go": banks use their capital to lend you money — enough to purchase the house — and you take the obligation to pay off your debt.

If you fail your payments, the bank can take ownership of the property. Once (and only) you pay off the entirety of the loan, you will have complete ownership (and, for example, sell the property).

## The elements of a mortgage

A mortgage consists of many elements, extremely intertwined. Start from this list: it covers the elements in order of importance".

• Principal (loan amount)

The principal is the amount of money that the bank will lend you. It depends on various factors, from the value of the property to your financial situation.

• Interest rate

The interest rate is the percentage of each payment the lender keeps for itself as compensation. The lower the interest, the lower the final sum you pay. To learn more about interest, check our compound interest calculator and real interest rate calculator.

• Loan term

The loan term is the "duration" of the loan. The term can vary widely, from 20- to 50 years. The longer the term, the smaller each payment will be; there's a catch, however: the final sum would be higher due to more interest payments.

• Interest calculation method

The lender decides the interest calculation method: this is how the interest is applied during the loan term. An interest that depends on the amount still owed to the lender gradually decreases with the payments, allowing for an acceleration of the payment rates.

• Payment frequency

The frequency with which you repay the loan affects the loan term and the final amount of money you pay to the lender. As a general rule, the higher the frequency, the lower each payment (though the monthly payments are higher), and the shorter the term.

## Other elements in the mortgage loan calculator

You can tweak your mortgage with additional parameters. These are, however, not necessary in the basic calculations.

• Prepayment

It may happen that you can pay a single bigger sum once, outside of your regular payments. This lump sum prepayment helps you repay your debt faster — but the bank may apply a commission on the payment due to their loss of some of the interest.

• Private mortgage insurance

Private mortgage insurance (PMI) protects the lender in case of a borrower's default. Insuring your loan is not always required: the lender may ask for it when your financial situation is not solid enough. A higher down payment, the amount of money you have before the beginning of the loan, ensures that the interest rate is low and you don't need a large PMI.

• Extra periodic payments and yearly increase

You can add extra payments outside the normal frequency, reducing the loan term. If your job is secure, you can ask the bank to consider the increase in your salary in your mortgage calculations. Ask beforehand to avoid paying unnecessary commissions on the added payments.

## How to calculate a mortgage: the mortgage formula

The formula to calculate your home loan is:

$\footnotesize MP = P\cdot \left(\frac{r\cdot (1+r)^n}{(1+r)^n-1}\right)$

Where:

• $MP$ is the monthly payment;
• $P$ is the principal;
• $r$ is the monthly interest rate; and
• $n$ is the number of months during your term (how many times you are supposed to pay $MP$).

The mortgage formula you see here is not the one we applied in our mortgage payment calculator: there, we implemented more complex formulas. The concept remains!

## How to use our mortgage calculator

Our mortgage calculator is fairly simple to use: insert the required values in our home loan calculator, and we will calculate the periodic payments. If you insert some of the additional elements of the mortgage loan, we'll calculate an updated periodic payment.

Here's an example: assume that:

• Your principal is $P = 150,000\ \text{\textdollar}$;
• You set up a loan term of 30 years, for a total of 360 months;
• Your annual interest is $5\%$. which equals a monthly interest, $r=0.004$.

Let's calculate your mortgage loan monthly payment:

\footnotesize \begin{align*} MP\! &=\! 150,\!000\!\cdot \!\left(\frac{\!r\cdot (1+0.004)^360}{(1+0.004)^360\!-\!1}\!\right)\\ &=787.00\ \text{\textdollar} \end{align*}

To find the total sum of your payment in this simple mortgage loan calculation, multiply the monthly payment by the number of the months in your loan term:

$\footnotesize360\cdot787.00=283,\!320\ \text{\textdollar}$

The cost of your loan is equal to the difference between the final sum and the principal:

$\footnotesize283,\!320-150,\!000=133,\!320\ \text{\textdollar}$

Our mortgage loan calculator doesn't only give you numbers but a neat graphical representation of the state of your house loan.

In the lower part of our home loan calculator, you will find a graph with three different data sets.

• The dark blue line is the remaining amount of money you need to pay;
• The light blue line is the amount of paid principal; and
• The orange line is the paid interest.

Below the graph, you can find a pie chart with the breakdown of your payment between principal, interest, insurance, and other costs.

At the bottom of our mortgage calculator, you will find a table with a complete breakdown of each regular payment: change the starting date freely to see how the proportions of your payment change.

## Disclaimer on our mortgage payment calculator

The result you see on our calculator can be different from the result of the mortgage formula. Moreover, they can disagree with the results of the calculations of your lender: use our calculator only as a guide!

Davide Borchia
Home value
$Down payment$
Down payment in percentage
10
%
Loan amount
$Interest rate % Loan term yrs Interest calculation method monthly (US & UK) Payment frequency monthly First day Payment 684.03$
Further Specifications
Extra periodic payment
$Yearly increase in payments % Starting from Lump sum prepayment$
Paid on
PMI
%
Total periodic payment
740.28
$Annual Balances Mortgage Summary Your mortgage payoff date is 29.07.2053. The total of the 360 mortgage payments is$246,249.
From that, the total interest payment is $111,249. The total payable Private Mortgage Insurance (PMI) is$4,106, with a $56 periodic contribution, that needs to be paid until 29.07.2029. Your total payment with all additional costs is$250,355.
Total Payment Breakdown in Percentage
Amortization Table
Due dates from
Due DateOpening BalancePayment (P+I)Principal AmountInterest AmountPMIOther costsTotal PaymentSum of PaymentsRemaining Balance
29.09.2023135,000684.03177.78506.2556.250740.28684.03134,822.22
29.10.2023134,822.22684.03178.44505.5856.250740.281,368.05134,643.78
29.11.2023134,643.78684.03179.11504.9156.250740.282,052.08134,464.67
29.12.2023134,464.67684.03179.78504.2456.250740.282,736.1134,284.89
29.01.2024134,284.89684.03180.46503.5756.250740.283,420.13134,104.43
29.02.2024134,104.43684.03181.13502.8956.250740.284,104.15133,923.3
29.03.2024133,923.3684.03181.81502.2156.250740.284,788.18133,741.49
29.04.2024133,741.49684.03182.49501.5356.250740.285,472.2133,558.99
29.05.2024133,558.99684.03183.18500.8556.250740.286,156.23133,375.81
29.06.2024133,375.81684.03183.87500.1656.250740.286,840.25133,191.95
29.07.2024133,191.95684.03184.56499.4756.250740.287,524.28133,007.39
29.08.2024133,007.39684.03185.25498.7856.250740.288,208.3132,822.14
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