Mortgage payment or EMI: same math, local extras

One loan, many names

Ask for a home loan in different countries and you will hear different words for the monthly payment.

• India calls it an EMI, short for equated monthly instalment. The word is also used for car loans, personal loans and phone purchases.
• The United States and Canada say mortgage payment. The loan is a mortgage, and the payment is often called principal and interest, or P&I.
• The United Kingdom often says repayment mortgage when the payment clears both interest and principal. An interest-only mortgage is a separate product.
• Australia talks about home loan repayments, usually on a variable or fixed rate.
• Germany uses the term annuity loan, or Annuitätendarlehen, for the standard home loan.
• The UAE uses mortgage and EMI interchangeably, with a rate that is often fixed for a short period.

The names differ, but the loan underneath is almost always a reducing-balance loan. You owe a balance. Each month interest is charged on that balance. Your payment covers the interest first, and the rest cuts the balance. Because the balance falls, the interest part falls, and the principal part grows. In the early years, most of each payment is interest. In the last years, most is principal.

The EMI calculator and the mortgage calculator both use this method. The guide to calculating EMI shows the formula step by step. The EMI answers page and the mortgage answers page cover common questions.

The formula behind every version

The standard formula is:

Payment = P × r × (1 + r)^n ÷ ((1 + r)^n − 1)

P is the loan amount, r is the interest rate for one period (usually a month), and n is the number of payments. For a 7.2% annual rate paid monthly, r is 0.6% a month. For a 20-year loan, n is 240.

You do not need to calculate this by hand. The point is to understand what each input does.

• A bigger loan raises the payment in direct proportion.
• A higher rate raises the payment, and the effect on total interest is larger than the effect on the payment.
• A longer term lowers the payment and raises total interest.

One example, two tenures

Take a loan of 100,000 at 8% a year. Only the tenure changes.

• 5 years (60 payments): about 2,028 a month. Total repaid about 121,700. Interest about 21,700.
• 10 years (120 payments): about 1,213 a month. Total repaid about 145,600. Interest about 45,600.

Doubling the term cut the payment by about 40%. It more than doubled the interest. This is the trade the EMI and mortgage calculators are built to show.

A longer tenure makes the month easier. It also keeps you in debt for longer and costs more in total. Neither is right or wrong. They suit different budgets and plans.

A bigger loan shows the same trade more sharply. Take 300,000 at 6.5%.

• 15 years: about 2,613 a month. Total repaid about 470,400. Interest about 170,400.
• 30 years: about 1,896 a month. Total repaid about 682,600. Interest about 382,600.

The 30-year payment is about 27% lower, and the interest is about 2.2 times larger. For many buyers the lower payment decides whether the loan is approved at all, and they plan to prepay when income grows.

What changes by country

The loan formula is shared. The details around it are local. This section lists what usually changes. Rules and rates move, so treat it as a map and confirm each point with a lender.

United States

• Escrow items. Property tax and homeowners insurance are often collected with the mortgage payment and paid by the lender on your behalf. The monthly bill is then principal, interest, tax and insurance, often called PITI.
• Private mortgage insurance. A down payment below 20% commonly triggers PMI, which adds to the monthly cost until the loan balance falls to a set share of the home value.
• Terms. Thirty-year and fifteen-year fixed-rate loans are standard. Adjustable-rate loans exist.
• Prepayment. Most conventional loans allow extra payments without a fee. Check yours.

Canada

• Compounding. Fixed-rate mortgages are quoted with semi-annual compounding, which makes the monthly payment slightly lower than a monthly-compounding calculation at the same stated rate. On a 400,000 loan at 5% over 25 years, the difference is about 12 a month.
• Terms and amortisation. The rate is fixed for a term, often 1 to 5 years, and then renewed. The amortisation, which is the full payoff period, is commonly 25 years.
• Stress test. Lenders may test affordability at a higher rate than the one you will pay.
• Prepayment penalties. Breaking a fixed-rate mortgage early can be costly.

United Kingdom

• Repayment versus interest-only. On 200,000 at 5% over 25 years, a repayment mortgage costs about 1,169 a month and clears the loan. An interest-only mortgage costs about 833 a month and leaves the full 200,000 owed at the end.
• Fixed periods. Many deals fix the rate for 2 or 5 years and then move to a higher standard rate unless you remortgage.
• Early repayment charges. These often apply during the fixed period.
• Fees. Arrangement and valuation fees can be added to the loan or paid up front.

Australia

• Variable and fixed rates. Variable rates are common, and a fixed period of 1 to 5 years is also offered.
• Offset accounts. Savings in an offset account reduce the interest charged on the loan, because interest is calculated on the balance minus the offset.
• Comparison rate. Lenders must show a comparison rate that includes many fees, so a low headline rate does not hide the cost.
• Interest calculation. Interest is commonly calculated daily and charged monthly.

Germany

• Annuity loans. You usually choose the interest rate, the fixed-rate period (often 10 years) and the initial repayment rate, such as 2% of the loan a year. The payoff time is the result, not the input.
• Example. On 300,000 at 3.5% with 2% initial repayment, the monthly payment is about 1,375. The loan takes about 29 years to clear, and about 228,000 is still owed after the first 10 years.
• Fixed-rate period. When it ends, you renegotiate the rate on the remaining balance.
• Buying costs. Notary, land registry and transfer tax add a meaningful amount to the cash you need.

India

• Floating rates. Most home loans float with a benchmark, so the EMI or the tenure changes when rates move.
• Fees. Processing fees are often between 0.25% and 1% of the loan, with GST on the fee. On a ₹50,00,000 loan, a 0.5% fee is ₹25,000, and 18% GST on it adds ₹4,500.
• Prepayment. Floating-rate loans to individuals often have no prepayment charge, while fixed-rate loans may.
• Tax benefits. Some deductions apply on interest and principal, with limits that change.

United Arab Emirates

• Rate resets. A fixed rate for the first 1 to 5 years is common, followed by a variable rate linked to a benchmark.
• Down payment. Minimum down payments depend on the buyer and the property.
• Fees. Registration, valuation and arrangement fees add to the upfront cost.

Switch the country menu on the calculators before you read the currency. For a country-by-country overview of what each calculator covers, read the guide to calculators by country.

What the payment still leaves out

A calculator shows principal and interest. A real month shows more. Add these to your sheet.

1. Property tax or local rates. Some countries collect it in the mortgage payment, others bill it separately.
2. Home insurance. Often required by the lender.
3. Mortgage insurance. PMI in the US, or lender's mortgage insurance in some countries, when the down payment is small.
4. Maintenance and repairs. A common planning figure is 1% of the home value a year, which is only a guide.
5. Service charges or ground rent on flats and leasehold homes.
6. Utilities and internet. Larger homes often cost more to run.
7. Moving and set-up costs. Furniture, fittings and small repairs after you move in.
8. Closing costs. Legal fees, taxes, valuations and lender fees, often 2% to 5% of the price, depending on the country.

The guide to mortgage basics for first-time buyers lists the costs that surprise people most often and the order in which they arrive.

Fixed, floating and hybrid rates

How the rate behaves matters as much as its level.

• Fixed rate. The rate and the payment stay the same for the fixed period. It gives certainty. It may cost more than a floating rate at the start.
• Floating or variable rate. The rate follows a benchmark. The payment, or the tenure, changes when the benchmark moves. It can be cheaper when rates fall and painful when they rise.
• Hybrid. A fixed rate for a few years, then floating. Common in the US, the UK, the UAE and India.

Test a floating loan at a higher rate. Take 300,000 over 25 years. At 6.5%, the payment is about 2,026. At 7.5%, it is about 2,217. A one-point rise adds about 191 a month. If your budget cannot absorb it, choose a smaller loan or a fixed rate if it is fairly priced.

Personal loans use the same formula

The same method works for loans that are not mortgages. A car loan, a personal loan and a consumer loan all reduce a balance with equal instalments. The differences are the rate and the term. Personal loans usually have higher rates and shorter terms.

Use the personal loan EMI calculator with the rate on your actual offer. Add any processing fee, because it is usually taken from the amount you receive. A 2% fee on a 500,000 loan costs 10,000 at the start, which raises the effective cost of borrowing.

Extra payments and early repayment

Almost every reducing-balance loan can be repaid faster. Extra payments go straight to principal, which cuts the interest charged on later months.

Take the 300,000 loan at 6.5% over 30 years. The payment is about 1,896. If you add 100 a month, the loan clears about 4 years early, and you save roughly 61,000 of interest. The exact figure depends on the loan, so run your own numbers.

Before you do, check three things:

• Whether the lender charges for early repayment, and for how long.
• Whether extra payments shorten the term or reduce the payment.
• Whether you have an emergency fund. Money in the loan is hard to get back.

A five-step process to compare loans across borders or lenders

1. Write down the loan amount, rate, term and rate type for each offer.
2. Run each in the calculator to find the payment, total repaid and total interest.
3. Add the local extras: property tax, insurance, mortgage insurance and fees.
4. Compare the total monthly outlay with your take-home pay, using the leftover-money method rather than a ratio alone.
5. Test a higher rate for any floating or short-fixed loan, and check what happens when the fixed period ends.

Do not compare a rate from one country with a rate from another. Interest levels, inflation and taxes differ, and a rate that is cheap in one place may be high in another.

Worked example from start to finish

A couple is buying a home priced at 375,000 in the United States. They have a 20% down payment.

Frequently asked questions