# How to Calculate Amortization

13 May 2019 by National Bank

When you borrow money to buy a house or carry out another personal project, amortization is a key element. Here are some basic concepts to consider before establishing how much time it will take to pay off your loan.

Amortization allows you to divide several payments for capital repayment and loan interests. The amount of each payment is the same and they are made periodically, often on a monthly or weekly basis, for a specific period of time.

For example, if a loan is spread out over eight years, amortization is the time it takes to reimburse the total capital and interests each month or each week at a fixed-rate amount. It has a financial impact on all types of loans with interest.

Although not discussed here, amortization also refers to an accounting operation used in the preparation of business’s financial statements and self-employed workers. It involves distributing the cost of goods over a few years rather than registering it in full the year of the purchase.

## How to calculate amortization

Three factors are taken into account for the calculation: the amount borrowed, the duration and the annual interest rate. You will find many online loan calculators that, in just a few clicks, can help you estimate the effects of amortization on a loan.

Are you curious about the logistics behind the math? Starting with the amount of your periodic payments, you can calculate the portions of interest and capital that you pay with each payment. Imagine that you borrow \$25,000 at 10% for 4 years at a monthly payment of \$634.06. First, convert the annual interest to a periodic rate: 10% ÷ 12 = 0.83%. Next, multiply the balance by this rate: \$ x 0.83% = \$207.50 in interest (for the first month) and \$426.46 in capital (\$634.06 - \$207.50).

Redo the next calculation, payment by payment, each time subtracting the capital repaid from the remaining balance. “When a loan is amortized, the interest is always calculated from the balance,” explains Louis-François Éthier, Director of Mortgage Products at National Bank.

## Interests and reimbursement of capital

Even if payments are equal, the portion that pays the interest on a loan is reduced progressively as the capital balance decreases. This is the principle of diminishing interest. If you take a look at the amortization table, you will notice that the parts corresponding to the capital repayment and interest payment vary from one deadline to the next.

The amount allocated to interest is at its maximum for the first payments and then gradually decreases. For a loan amortized over a long period, such as a mortgage loan, payments during the first year are used to pay interest rather than repay capital.

For example, if you borrow \$200,000 at 5.49% over 25 years to buy a house, only around the 12th year will you begin to pay more capital than interest. On the other hand, with a personal loan of \$20,000 at 10.15% over 5 years, the capital repayment will exceed the interest starting with the first payment.

“It’s a simple mathematical question,” says Louis-François Éthier. “The longer the amortization, the less the loan is repaid quickly and the more interest there is to be paid. The shorter it is, the less you pay for it.”

## Save on a mortgage loan

A mortgage is often the most important amount of money a person will borrow in their life. “At National Bank, the maximum amortization period for a mortgage loan is 30 years,” explains Louis-François Éthier. “However, most people choose to pay off their home over 25 years.”

This 5-year difference will save you a lot of money. A mortgage loan of \$200,000 amortized over 25 years rather than 30 reduces the total interest paid by \$38,000. The online calculator allows you to do simulations with different amortization periods.

In most cases, however, it is better to exercise caution by opting for a longer period, which is what Louis-François Éthier recommends. “The shorter the amortization, the higher the periodic payments. You need to ensure that your budget allows for this.”

Above all, even if you have chosen a longer term, you can always opt for accelerated repayment. “These options go directly to the return of capital and thus reduce the length of amortization and the interest,” explains Éthier. “When you have a little extra in your budget, it’s very beneficial.” You can make an additional payment, make an early repayment or even increase the amount of your payments. Because certain restrictions apply, depending on the type of loan, speak with your advisor to establish the best strategy.

## Car loan

You also need to consider amortization when you buy a car with a loan. If you are looking to pay the lowest payments possible, take time to do some calculations before you make a decision. The smaller your payments, the longer your amortization and the more you will pay in interest.

For example, interest on a car loan of \$31,640 at 6.34% over 7 years would total \$7,557. If the loan is amortized over 5 years, the interest would be \$5,299. You would save \$2,258 by reducing the loan term by two years. However, payments would change from \$107.34 a week to \$141.50.

You also need to consider depreciation, which is the difference between the purchase price and the resale price. The moment a car leaves the dealership, it begins to lose value. A new vehicle loses half of its value in three years. Depreciation then continues at a rate of about 8 to 10% per year. Consider this when the time comes to choose the amortization period. Can you afford to make higher payments? Opt for a shorter amortization, unless you decide to keep your vehicle longer. Otherwise, if you amortize your loan over seven years and you resell your vehicle after 36 months, its resale value could be lower than the balance of your debt. In the previous example, the vehicle for which you paid \$31,640 will have an estimated value of \$15,820, while the debt would amount to \$19,770. Amortized over 5 years, the latter would be \$13,866.

## Personal loan

“A personal loan helps pay for short-term expenses, such as renovations, travel or a wedding,” says Éthier. “The amortization period does not exceed five years.” Because it is not secured by assets used as collateral, as is the case with a car or mortgage loan, a personal loan often requires a higher interest rate.

Whether a mortgage loan, person loan or even a car loan, amortization has a significant impact on the total interest you will pay. Don’t hesitate to discuss this with an advisor at your bank to weigh the pros and cons of choosing a shorter or longer term. Together, you can consider different scenarios.

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