# Mortgage Calculator

Created by Mateusz Mucha, Joanna Andrzejewska, Tomasz Jedynak, PhD and Tibor Pál, PhD candidate
Reviewed by Bogna Szyk and Jack Bowater
Based on research by
Cipra T. Financial and Insurance Formulas; 2006
Last updated: Jul 19, 2023

This mortgage calculator is a well-equipped loan calculator that deals with multiple questions arising when you are about to buy a house with a mortgage loan. As the primal function, it enables you to estimate your payment with different loan constructions and compare them alongside its connected costs, especially its interest payments. With the dynamic chart built in the calculator, you can easily follow the progression of your yearly balances and its alteration in case of accelerated payment or different prepayment methods. Besides, the mortgage summary gives you a detailed picture of your mortgage loan with comparisons from different angles. For simplicity, we also designed a diagram that displays how your loan relates to other costs emerging from your mortgage. Lastly, the amortization table allows you to analyze your balances in each due date in a specific interval.

If you read further, you can learn what mortgage definition is, how to calculate a mortgage payment, and what are the common types of mortgages. Besides, we explain all features of the calculator and its background; for example, you can check what the mortgage payment formula is and how does the mortgage amortization operate. Also, we give you some hint about the current mortgage rates in different loan constructions.

In case you would like to use a less sophisticated tool, you may check out the above calculators created on this topic.

Also, you may check our HELOC calculator if you are specifically interested in a home equity line of credit.

## What is a mortgage?

Formally, a mortgage loan (or simply mortgage) is a legal agreement where a bank (or other authorized institution) lends money to the borrower in exchange for taking the title of the debtor's property. The bank holds this title until the debtor fully repay the whole loan.

The essential part of a mortgage besides the loan amount (principal) is the interest, which is the cost of the loan for the debtor, and the remuneration for the bank. In other words, we can say that a mortgage is a form of a personal loan that the bank provides for the house purchase. The characteristic feature of each mortgage is setting the collateral on the real estate the debtor buys. It means that if the debtor is unable to realize the periodic payments (installments) at the agreed due dates, the lender can take ownership of the property.

The most typical layout for repaying a mortgage loan is to make equal payments that consist of an altering part of principal and interest over the agreed term. This kind of schedule generally corresponds to amortization loan in the US and Canada or repayment mortgage in the UK. From the perspective of the lender, a mortgage is a type of annuity, which is based on the time value of money formula.

Since we designed this mortgage calculator for estimations related to the amortized type of mortgage mentioned above, in the following, we focus mostly on this type of loan. Still, it is worth to know that a mortgage might have other repayment structure that involves different calculation procedures. Such arrangements are, for example, interest-only, reverse mortgage, or balloon payment mortgage.

## How to choose a mortgage?

Before you take a mortgage, you need to know how different factors and components affect your loan. Besides, to be able to apply this calculator properly and to understand its computational background, it is crucial to get familiar with the following terms.

• Principal

It is merely the amount you want to borrow from the bank. Its amount depends on two factors: the home value (the price of the property) and the down payment.

• Down payment

It is the amount of money you already have and able to use to pay for the property before you get the loan. Its level is an essential aspect when applying for a mortgage as it often represents the main obstacle to get the loan. The required minimum amount varies depending on the institution and the country's legislation. In the US, for example, the down payments range from 3,5% (FHA loans) to 20-25% of the purchase price. But that's not all. Since lower initial payment usually associates with higher risk to the lender, its sum also affects the interest rate. Thus, the more you pay from your savings, the lower the rate is. It is strongly connected to the LTV (loan-to-value) ratio, which indicates the ratio of the loan amount to the value of the property. So, if you see a 70% LTV offer, this means that you can borrow 70% of the purchase price while the minimum deposit is 30%.

• Interest rate

It typically refers to the advertised annual rate of interest that is one of the most relevant factors you need to take into account when choosing a mortgage. It is worth to mention that the yearly interest rate is a nominal rate, that does not represent the real rate of interest. Therefore it is not always the best measure to express the true cost of your loan. The reason is that it doesn't incorporate additional factors that might alter the actual rate of interest charged on your mortgage. Such factors is, for example, the function of compounding and its frequency that indicates how often the interest is applied to the principal. If compounding occurs more often than yearly (as in the case of most loans), the actual interest amount in a year becomes higher. By incorporating the effect of compounding, the Annual Percentage Yield (APY), or with another term, the Effective Annual Rate (EAR) gives you a better guideline in this relation. Another useful indicator is the Annual Percentage Rate (APR), which takes into consideration the fees and other charges involved in the loan.

• Loan term

It is the interval in which you obliged to repay the borrowed money and fulfill the condition set out by the contract. Loan terms vary depending on the bank and mortgage type (fixed-rate mortgage have shorter terms than variable rate). Usually, one can take a loan for up to 20 or even 30 years, but some mortgages might last for 40 or 50 years. The loan term influences mortgage conditions. The longer the duration, the less you need to pay periodically, but eventually, you pay more since the bank charges interest for a more extended period. It is important to note that in some particular cases, you may pay off the principal amount faster. In this way, the amortization term, which is the actual length of time of mortgage payoff, will be shorter than the original term of the loan, and the paid interest became smaller.

• Interest calculation method

It refers to the prevailing practice of how interest is handled during the loan term. More precisely, it is the compounding frequency - the regularity with which your lender applies the annual rate of interest to the principal's balance. The expression of compounding interest, however, is slightly misleading in this context. While in the case of a savings account, the base of compounding includes the interest beyond the principal, with amortization mortgages, the compounding effect comes solely from the varying principal payments. Since you are paying back the mortgage in equal parts, your installment includes a higher portion of interest at the beginning of the loan term. As you proceed with the loan repayment, the structure of your payments changes: in each period, the calculated interest gradually decreases, as you owe to the bank less money. In turn, this procedure allows for more of the principal to be repaid at each installment, leading to an accelerating drop in your remaining balance. You can easily observe this phenomenon on the graph of Annual Balances, as well as in the Amortization Table, which gives you a detailed picture of this matter.

• Payment frequency

When it comes to the schedule of your payments, you have multiple choices. It is worth to keep in mind that the higher payment frequency does not have a significant impact on your total interest and amortization term. For example, if your monthly payment is 200 dollars, but you decide to pay 100 dollars semi-monthly instead, the only gain comes from the compounding effect mentioned previously. The real difference appears, however, when the higher payment frequency matches with a higher than proportional installment. There are two types of repayment schedules that provide you such an option. The accelerated bi-weekly payments are exactly half of the monthly payment but collected every second week that means on each 14th day of the amortization term. Since a regular month has more than 28 days (except February, which is not in a leap year), you will have at least twice a year three payments in a month. Staying at the previous example, it means that you pay 100 dollars 26 times in a year, which equals an extra 200 dollars in a year. You may reach a similar result with an accelerated weekly schedule. In this case, your payment is the quarter of the monthly amount, but they are made precisely every seven days. In both cases, you pay a little more on a monthly bases, but the result is a faster repayment of the principal. Thus, after all, the amortization term shortens, and the lender can charge significantly less interest. For better insight, the below table summarizes the different payment scenarios with the resulting interest savings for a US mortgage of 100,000 dollars with a 5 percent interest rate and 20 years loan term.

Prepayment Frequency

Periodic Payment

Annual Payment

Amortization Term

Interest Savings

Monthly

$659.96$7,920

20 years

$0 Semi-monthly$329.63

$7,911 20 years$165

Bi-weekly

$304.25$7,911

20 years

$177 Acc. Bi-Weekly$329.98

$8,579 17 years 6 months$8,349

Weekly

$152.05$7,907

20 years

$253 Acc. Weekly$164.99

$8,579 17 years 6 month$8,464

• Prepayment

As we mentioned before, the most effective way to moderate the financial cost of your mortgage is to reduce the balance of the principal and so shorten the amortization term. There are two prominent ways to realize this: You may increase your regular installment (extra periodic payment), or you may pay a single amount at a specific date (lump sum prepayment). In both cases, the extra money directly affects your principal balance, that is, reducing the base for the interest calculation. You always need to keep in mind, however, that the bank may charge you an additional fee for compensating their lower interest revenue. Therefore, you should always consult with your lender in case of any advanced payment before the agreed due date.

• PMI or Private Mortgage Insurance

This insurance aims to protect the lender in case a borrower defaults on a mortgage loan. Real estate mortgage companies in the US typically require to involve in such agreement when the down payment is less than 20 percent of the home value. It usually costs between 0.5% to 1% of the entire loan amount on annual bases. When the total equity (the financed part of your home) reaches 20 percent of the home value, the PMI might be canceled. The administrative procedure what the borrower needs to initiate, however, may take several months and require a formal appraisal of your home beforehand. To sum up, it is always better to enter into a mortgage contract with a larger down payment that reduces not only your interest charges but also eliminates PMI expenses.

• Property Tax

In the US, its rate stands around 0% to 4% of the home value, depending on the location of your home. It covers expenses arising locally, for example, local education, local governments, and infrastructure. In some countries (like US) if you have a low down payment the lender will set up an escrow account to collect any additional expenses, which will be included in your installments.

• Homeowner insurance

It is a type of property insurance that covers losses and damages to the real estate and its accessories or other accidents in the home or on the property.

• HOA or Homeowners Association Fee

It is stand for homeowners association fee which is must be paid monthly by owners of certain types of residential properties, usually condominiums. The HOAs collect these fees to assist with maintaining and improving properties in the association.

• Other costs

You can add here all additional expenses that are not included explicitly in our calculator. For example, some banks will make you buy insurance against unemployment and other personal risks. It all depends on the bank's imagination. Besides, the lender may offer better terms in return for you buying additional products. (Credit cards, personal accounts, etc.) Usually, you will need to use them throughout the whole term of your loan.

## How to use Mortgage Calculator?

Now that you know the basics, we can get to our calculation. Please note, however, that due to possibly missing factors, the estimated results may diverge from the final values that the bank charge when providing a loan.

1. First, you need to set the home value and the down payment which together will give you the amount of the loan amount for financing the home purchase. This value will be the initial amount of the principal that you need to repay during the given loan term.

2. Fill in the interest rate.

3. After setting the interest calculation method and the desired payment frequency you can see what your periodic payment will be.

4. In the section of Further Specifications, you can set additional features mentioned previously, which will be included in the total payment in a given period. Note that you can reach some of the variables in the advanced mode.

After specifying your mortgage you will have several option to analyze the results.

• Annual Balances

On this graph, you can easily follow the progression of your yearly balances. You can check what will be your paid principal and paid interest at the year ends as you proceed in the loan term. Besides, it also shows how much money remained to be paid. In case you set an accelerated payment or any option for prepayment, the chart will also display the year when you pay off the whole loan.

• Mortgage Summary

In this section, we give you fascinating details for further consideration. For example, you can learn what will be your exact pay off date, how many installments you need to make, what is the total value of your mortgage, and what is its total interest. Besides, you can check how much interest and time you can save if you choose an accelerated schedule or pay extra money.

• Total Payment Breakdown in Percentage

We designed this simple graph to demonstrate how your total mortgage is built up. With a quick sight, you can see how the total interest, private mortgage insurance, and other costs related to the original loan amount.

• Amortization Table

This comprehensive table will be in your assistance if you would like to check any detail on your balances at a specific date. By setting a particular day, the table will display all scheduled due dates for one year onward with all financial figures.

Remember, when taking a mortgage, you need to think about all the possible costs that the bank charges or requires. It is particularly essential in case of long term mortgages combined with a low down payment. Still, if you encounter any further expense, you can add as an other costs to the computation.

## Mortgage payment formula

If you would like to know how to calculate a mortgage payment on your own, the equation is the following. For the matter of simplicity, we represent here a simplified version of the equation that doesn't incorporate all features involved in the calculator.

MP=P[r(1+r)n/(1+r)n-1]

• MP = monthly payment
• P = principal
• r = monthly interest rate
• n = number of months you will have to repay your loan for

To calculate your monthly interest rate simply divide the annual interest rate by 12.

Let's do an example calculation. To do that, we need to know: the principal amount, monthly interest rate, loan period/number of payments. You can find this information in your mortgage loan agreement. For our purposes, we will assume the following numbers:

• our principal (P) equals 100 000 EUR
• our loan period is 20 years - that is 240 months, therefore "n" = 240
• the annual interest rate amounts to 5%, this divided by 12 equals 0.004 (0,05/12) and this is our "r"

Now, we can get on with the calculation:

MP=100 000[0.004(1+0.004)240/(1+0.004)240-1]

To make it easier, we will add 1 to the "r"

MP=100 000(0.004*1.004240/1.004240-1)

In the next step we have to raise the "(1+r)" (in our example 1,004) to the power of "n" (in our example 240). It is best to use a calculator (put in the value to be raised, than press the xy button and enter the "n" value, then press "=") or an excel sheet (use the POWER function: =power(number to be raised,power). The number in our case is: 2.607. Now our equation would look like this:

MP=100 000(0.004*2.607/2.607-1)

Let's simplify again and multiply the "r" times the result of raising to power (the top value) and subtract "1" from the result of raising to power on the bottom:

MP=100 000(0.01043)/1.607

All that is left to do now is to divide the numerator by the denominator...

MP=100 000*0.006490

...and there you go: your monthly payment is 649.03. If you want to know what the total sum of all your payments will amount to, just multiply your monthly payment (MP) by the number of months you will pay your loan (n). In our example it would be:

649.03*240=155767.2

When you know what your total payments will be, you can also calculate how much you will pay the bank for loaning you money. Just subtract your principal from your total payments. In our case the costs of our loan would amount to 55 767.2 EUR.

You can also forget about all this long counting and use our mortgage calculator.

## Fixed vs. variable rate mortgage

While choosing a mortgage there are more things to consider than just the interest rate and fees. You also need to decide what type of mortgage you want. There are of course many variations but the main two types are:

• Fixed rate - the interest rate will stay the same throughout the whole mortgage term.
• Variable rate - the interest rate will change (usually, it is linked to the national bank's base rate or the reference interest rate on the inter bank market).

A peace of mind is the biggest advantage of the fixed rate mortgage. You can be sure that your rate will stay the same and plan your expenses with more accuracy. Keep in mind however, that fixed rates are usually a bit higher than variable ones. And, if the rates fall, you won't benefit from it.

The advantages of variable rate mortgages lie in its flexibility - when the base rate falls, your interest falls as well, if you want to overpay and get out early, you can. Ironically, flexibility is also their main disadvantage - if the base rate goes up, so does your interest, thus it is more difficult to plan your expenses and you need to remember to have some extra money should the rate go up.

## Balloon payment mortgage

Balloon payment mortgages are a special kind of mortgage where you are left with a large payment at the end of the loan. This means that the mortgage does not fully amortize over its lifespan. Balloon payment is always higher than monthly payments. It could amount to 2 times the monthly payment but it could also be thousands of dollars. In some cases, the payment is divided into a couple of smaller ones but usually, it is one lump sum paid at maturity. Balloon mortgages can have fixed or variable rates. Due to the high risk for small owners balloon loans are more common in commercial real estate, as an average homeowner could find it difficult to repay the balance due at the loan's maturity. However, there are ways to overcome this difficulty. Some borrowers simply plan to sell their house before the balloon payment is due, others plan to refinance their mortgage when the balloon payment is due. If you decide to do this, the lender will convert your remaining balance into a traditional fully amortized loan. There are balloon mortgages which refinance the remaining balance automatically - they are called "two-step" mortgages. If you are considering a balloon loan, check our partially amortized loan calculator to help you estimate how much it will cost you.

There are of course advantages to balloon loans, such as lower interest rates and monthly payments. Sometimes, it is also possible to take a bigger loan than if you were taking a standard fixed or variable rate mortgage. You need to be careful however, because you might not be able to sell your house before the maturity date or the prices in the housing market might fall substantially and you will lose money. There is also risk attached to refinancing. If your financial situation deteriorates or the interest rates have gone up in the interim you might be faced with unaffordable terms.

## Reverse mortgage

A reverse mortgage is a type of mortgage loan for a senior homeowner. Simply speaking, a reverse mortgage is a financial service which allows the homeowner to exchange their property for money. A reverse mortgage enables the property owner to release the funds accumulated in his home while maintaining the right to live in it. Formally we can say that thanks to a reverse mortgage, an illiquid asset (the house) becomes a source of liquid cash which can be used for consumption by the retiree.

Note that usually, the borrower is still responsible for maintaining the home, paying the property taxes and homeowner's insurance.

One specific feature of a reverse mortgage is that even though it is a type of a loan, it does not have to be repaid until the debtor passes away or moves out. At that time, the homeowner or the heirs can repay the balance of the reverse mortgage, or sell the house to pay off the balance.

The amount of money you can get from a reverse mortgage depends on many factors. Among them, the most important are: the age of the borrower, the interest rate, and value of the home. In some countries, there are also some lending limits imposed by the government.

Usually, the reverse mortgage loan can be received in the form of:

• Term payments – monthly payments paid during a specific number of periods (months, years),

• Tenure – monthly payments paid for the life of the agreement,

• Line of credit – you can draw from it as needed up to the maximum amount,

• Lump sum – a one-off payment paid when the agreement is closed.

It is also possible to combine the above options.

Generally, there are two models of financial products which are commonly named reverse mortgage:

• Loan model (a standard reverse mortgage, also known as lifetime mortgage, reverse mortgage loan, home equity conversion mortgage). In this model a loan taken by a borrower (homeowner) is repaid from the money acquired from the sale of the estate after his death.

• Sale model (also known as lifetime cash benefit, annuity for life, home reversion, reversion plan, annuity for life). In this model, the ownership of the property is transferred to the bank (or another financial institution) when the agreement is signed. In exchange, the borrower has the lifetime right to use the property and receives a lifetime stream of money from this transaction which he can use as an additional source of income in retirement.

Mateusz Mucha, Joanna Andrzejewska, Tomasz Jedynak, PhD and Tibor Pál, PhD candidate
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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 13.04.2054. 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 13.04.2030. 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
13.06.2024135,000684.03177.78506.2556.250740.28684.03134,822.22
13.07.2024134,822.22684.03178.44505.5856.250740.281,368.05134,643.78
13.08.2024134,643.78684.03179.11504.9156.250740.282,052.08134,464.67
13.09.2024134,464.67684.03179.78504.2456.250740.282,736.1134,284.89
13.10.2024134,284.89684.03180.46503.5756.250740.283,420.13134,104.43
13.11.2024134,104.43684.03181.13502.8956.250740.284,104.15133,923.3
13.12.2024133,923.3684.03181.81502.2156.250740.284,788.18133,741.49
13.01.2025133,741.49684.03182.49501.5356.250740.285,472.2133,558.99
13.02.2025133,558.99684.03183.18500.8556.250740.286,156.23133,375.81
13.03.2025133,375.81684.03183.87500.1656.250740.286,840.25133,191.95
13.04.2025133,191.95684.03184.56499.4756.250740.287,524.28133,007.39
13.05.2025133,007.39684.03185.25498.7856.250740.288,208.3132,822.14
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