Car Loan Calculator: The Monthly Payment Is the Wrong Number

A dealer will tell you a $45,000 car is "affordable" because it comes to $778 a month. What stays off that page: the term is 72 months, the rate is 7.5 percent, and the interest adds up to $11,020. You are buying a $56,020 car.

I do not care much for the monthly payment as a number. It is the one figure in the deal the seller controls completely, because the term can be stretched until the payment fits. The total you pay and the rate you pay are the two numbers that matter, and this post shows how to get them before anyone else does. The examples use dollars; the arithmetic is the same in euros.

The Loan Calculator runs the formula below and shows the full payment schedule. Put the offer in, change one input at a time, and watch what moves.

The formula, worked once

Monthly payment:

M = P × [r(1+r)ⁿ] / [(1+r)ⁿ - 1]

M is the monthly payment, P the amount you borrow after the down payment, r the monthly rate (annual rate divided by 12) and n the number of payments.

A $30,000 car, $5,000 down, 6 percent APR, 60 months:

• P = $25,000
• r = 0.06 / 12 = 0.005
• n = 60

` M = 25,000 × [0.005 × (1.005)^60] / [(1.005)^60 - 1] M = 25,000 × [0.005 × 1.3489] / [1.3489 - 1] M = 25,000 × 0.006744 / 0.3489 M = $483.32 per month `

Total paid: $483.32 × 60 = $28,999. Interest: $3,999 on a $25,000 loan.

So the $30,000 car cost $33,999 by the time the loan is done. The Percentage Calculator turns that into a share: 13.3 percent of the price went to the lender. Stretch the same loan to 72 months at 7.5 percent and the interest share passes 20 percent.

A longer term lowers the payment and raises the price

The same $25,000 loan at 6 percent APR over different terms:

| Term | Monthly | Interest | Total paid | |------|---------|----------|------------| | 36 months | $761 | $2,380 | $27,380 | | 48 months | $587 | $3,182 | $28,182 | | 60 months | $483 | $3,999 | $28,999 | | 72 months | $414 | $4,831 | $29,831 | | 84 months | $365 | $5,678 | $30,678 |

Going from 36 to 84 months cuts the payment by $396 and adds $3,298 in interest. The cheapest monthly is the most expensive line in the table.

A long term also keeps you under water for years. A new car loses roughly 15 to 20 percent of its value in the first year and around 10 percent a year after that. On a 72-month loan with nothing down, you owe more than the car is worth for the first three to four years. Sell it or write it off in that window and you pay the difference yourself.

What a down payment buys

The same $30,000 car, 6 percent APR, 60 months:

| Down | Loan | Monthly | Interest | |------|------|---------|----------| | $0 | $30,000 | $580 | $4,799 | | $3,000 (10%) | $27,000 | $522 | $4,319 | | $6,000 (20%) | $24,000 | $464 | $3,839 | | $9,000 (30%) | $21,000 | $406 | $3,359 |

Twenty percent down saves $960 in interest against nothing down. The larger effect is not the interest. It is that you almost never owe more than the car is worth, and that is what protects you when you sell early or the car is written off.

The old rule is 20 percent down on a new car and 10 percent on a used one. If that is out of reach, the honest reading is that the car is too.

There is a counter-argument. Run it before you decide. The Compound Interest Calculator shows what the same $6,000 does if you invest it instead: at 8 percent for 5 years, about $8,816. Set that gain against the $960 of interest saved and investing wins on paper. It only wins in practice if the money is actually invested, at that return, and stays there. I would still put it in the car unless the loan rate is very low.

Negotiate the price, not the payment

• Get a rate before you walk in. Ask your bank, or an online lender, what they would charge you. That number is your floor. Dealer finance sometimes beats it and sometimes does not, and either way you know which.
• Fix the total price first. Only then talk about financing. The question "what payment are you looking for" is how a $3,000 overprice disappears into 72 months.
• Decide about add-ons at home. Extended warranty, gap insurance, paint protection. They are sold at the desk after you have already said yes to the car, which is the worst moment to evaluate anything.
• Consider two or three years old. A used car with most of the factory warranty left often costs a third less than the same model new, and the steepest drop in value happened to someone else.
• Timing helps a little. End of month, quarter and year is when sales targets bite. It is not a big lever, but it is free.
• Your credit history sets the rate. The gap between the best and the worst tier is often five points or more. Fix what you can there before you sign, not after.

In the Netherlands most people do not finance through the dealer at all. A persoonlijke lening (a fixed-rate personal loan) from a bank, or private lease, are the usual routes. The same rule applies to both: compare the total over the term, not the monthly figure.

FAQ

How much car can I afford?

The rule I would use: everything the car costs per month (payment, insurance, fuel, maintenance, road tax) under 15 to 20 percent of take-home pay. On $5,000 a month that is $750 to $1,000 in total, which leaves room for a payment of roughly $400 to $600 once the rest is counted.

Cash or finance?

If the loan rate is low and you would actually invest the cash at a higher return, finance. If the rate is above 7 percent, or the cash would sit in a savings account, pay cash. Not having a payment at all is worth something too.

Should I refinance?

When rates have dropped since you signed, or your credit history has improved. Compare the interest left on the current loan with the interest on the new loan plus any fees. Lower total, refinance. Otherwise leave it.

APR or interest rate?

On most car loans they are the same, because there are no fees rolled in. When a dealer adds documentation or arrangement fees, the APR comes out above the stated rate. Compare offers on APR only.