How car loan repayments are calculated

Most car loans in New Zealand are repaid in equal instalments. You borrow an amount, you agree a rate and a term, and you pay the same amount every week, fortnight or month until the loan is gone. That sounds simple, but the number it produces often surprises people. This page shows where it comes from.

If you would rather see the result than read about it, the car loan repayment calculator on the home page does the working for you and updates as you type.

The four things that set your repayment

Every equal-instalment loan comes down to the same four inputs.

The amount you borrow. This is the car price, less any deposit or trade-in, plus any fees the lender adds to the loan. A bigger loan means a bigger repayment, and the effect is direct. Borrow twice as much at the same rate and term and the payment doubles.

The interest rate. This is the yearly rate the lender charges. It is split across your payments, so a weekly loan uses one fifty-second of the yearly rate for each week, and a monthly loan uses one twelfth for each month.

The term. This is how long you take to pay the loan off. A longer term lowers each payment but means you pay interest for longer, so the total cost goes up.

How often you pay. Weekly, fortnightly and monthly give a different number of payments over the same period. Five years is 260 weekly payments, 130 fortnightly payments or 60 monthly payments.

The formula

For a loan with no balloon, the repayment is:

payment = amount x rate per period / (1 - (1 + rate per period) to the power of minus the number of payments)

The rate per period is the yearly rate divided by the number of payments in a year. The number of payments is the term in years multiplied by the payments in a year.

You do not need to do this by hand. The point is to see what it is built from. The amount and the rate sit on top, so a bigger loan or a higher rate pushes the payment up. The number of payments sits in the exponent on the bottom, so more payments pull the payment down. That is why stretching the term makes each payment smaller.

A worked example

Take a $20,000 loan at 12.95% a year over five years, paid monthly. The 12.95% is only an example rate. Use the rate on your own quote.

• Rate per month: 12.95% divided by 12 is about 1.079% a month.
• Number of payments: 5 years x 12 = 60.
• Put those through the formula and the payment comes to $454.55 a month.

Over the whole loan you pay 60 x $454.55, which is $27,272.98. Take off the $20,000 you borrowed and the interest comes to $7,272.98.

The same loan paid weekly is 260 payments of $104.59, and the total repaid is $27,192.97. That is about $80 less in interest than paying monthly, because the balance comes down a little sooner.

Where each payment goes

Every payment has two parts: interest, and the part that pays off the loan. The payment stays the same size, but the split changes.

In the first month of the example, you owe the full $20,000. Interest for that month is about $215.83. The rest of the $454.55, which is $238.72, pays off the loan.

By the last month, you owe very little. Interest is under $5 and almost the whole payment, about $449.70, pays off the loan.

This is why paying a loan off early saves the most when you do it early. The money you save is the interest that would have been charged on the balance in the months you skip. Near the end of a loan there is very little interest left to save. A lender may also charge a fee for paying off early, so read your contract before you do.

What happens when you change one thing

Using the same $20,000 loan at 12.95%, paid monthly, here is what each change does.

• Shorter term, three years. The payment goes up to $673.40 a month, but the interest falls to $4,242.31.
• Longer term, seven years. The payment drops to $363.30 a month, but the interest climbs to $10,516.85.
• Lower rate, 9.95%. The payment drops to $424.45 and the interest falls to $5,466.94 over five years.
• Higher rate, 14.95%. The payment rises to $475.27 and the interest climbs to $8,516.43.

The pattern is the same each time. Anything that lowers the payment by stretching the loan out costs more in total. Anything that lowers the rate or the amount borrowed lowers both the payment and the total. A bigger deposit works the same way as borrowing less, so it cuts both.

Balloon payments

A balloon is a lump sum you still owe on the last day of the loan. Because you are not paying the whole loan off during the term, each regular payment is smaller.

With a $5,000 balloon on the same $20,000 loan at 12.95% over five years, the monthly payment falls from $454.55 to $394.87. That looks better, but you still owe $5,000 at the end, and interest is charged on it for all 60 months. The total you pay rises to $28,692.24, which is more than the $27,272.98 without a balloon.

A balloon can suit someone who knows they will have a lump sum at the end, or plans to sell or trade the car. It is worth checking you can find the money when the day comes. If you cannot pay it, you may need to refinance the balloon, and that has its own costs.

Fees and other costs

The formula above covers the loan itself. Lenders may add set-up fees or other charges, and if these are added to the loan they are borrowed too, which raises the repayment and the interest. Our calculator has a field for fees added to the loan. If a lender takes the fee in another way, such as paying it upfront, leave that field alone.

The figure to ask any lender for is the total cost of the loan, written down, covering every fee over the full term. Two loans with the same rate can cost different amounts once fees are counted, so compare totals and not just the repayment.

Insurance is a separate cost again. It is not part of the repayment formula, but you will need to budget for it, along with registration, warrant of fitness, fuel and servicing.

Why a lender’s figure may differ

If you use a calculator and then get a quote, the two numbers can differ a little. The usual reasons are below.

• The rate is different. A lender sets the rate from your own situation, and it may not be the rate you tried.
• Fees are included in one and not the other.
• Rounding or the exact payment dates differ.
• The lender uses a slightly different method for the first payment, for example when the first payment date is not a full period away.

None of these means the calculator is wrong. It means a calculator is a good guide and a quote is the real number. Use the calculator to get close, then compare actual quotes.

Checking the number against your budget

A repayment you can calculate is not always a repayment you can afford. Before you commit, check the payment against what you actually have left after rent or mortgage, food, power, insurance and your other debts. Allow a buffer, because costs move around. If the number is tight, a longer term lowers the payment but costs more overall, so a cheaper car or a bigger deposit is often a better fix.

If you are already finding repayments hard, do not wait. Talk to your lender early, because many have hardship options. Free, confidential help is available from MoneyTalks on 0800 345 123.

Sources

• Sorted, the Commission for Financial Capability’s money guidance for borrowing and budgeting basics
• Consumer Protection NZ for your rights when you borrow
• MoneyTalks for free financial help