Loan Amortization Schedules: Why Year One Barely Moves the Balance

You borrow $300,000 at 6 percent over 30 years. The payment is $1,799 a month. After a year you have paid $21,584 and the balance reads $296,316. Twelve payments, and the debt moved by $3,684.

Nothing went wrong. That is what an annuity loan does, and once you can see the split inside each payment you can decide where an extra euro or dollar does the most work. That is what this post is for.

I have tested mortgage administration systems, and the schedule is the first thing you check. If month one's interest is not the balance times the rate divided by twelve, everything after it is wrong too. The Loan Calculator builds the same schedule for any amount, rate and term, and lets you add an extra payment to see what changes.

Interest is charged on what is left, every month

Each month the lender charges interest on the remaining balance. Month one of the $300,000 loan:

$300,000 x 6% / 12 = $1,500

The payment is $1,799, so $299 is left over to reduce the balance. You now owe $299,701.

Month two charges interest on the new balance:

$299,701 x 6% / 12 = $1,498.51

Now $300.49 goes to the balance. The repayment share grows by about a dollar and a half a month at this stage. By month 300 the balance is about $93,000, the interest charge is $465 and $1,334 of the payment is repayment. In the last year almost the whole payment is repayment, because there is almost nothing left to charge interest on.

This is arithmetic, not a trick by the lender. Any loan with a fixed payment and interest on the outstanding balance behaves this way. It also tells you where extra money works hardest: at the start, when the balance is highest.

One Dutch aside, because it changes the picture. A Dutch mortgage comes as an annuïteitenhypotheek (annuity mortgage: fixed payment, the loan above) or a lineaire hypotheek (linear mortgage: fixed repayment). On a linear loan you repay the same amount of principal every month, so the payment starts higher and falls every month, and the total interest is lower. The front-loaded interest in this post is a feature of annuity loans, not a law of nature.

Read the total interest column first

A schedule has six columns per payment: the payment number, the payment, the interest share, the repayment share, the balance afterwards, and the interest paid so far.

The last one is the one to read. For the $300,000 loan at 6 percent over 30 years, total interest comes to $347,515. You repay more in interest than you borrowed.

Move any of the three inputs and that column moves a lot:

• 5 percent instead of 6: total interest $279,767, a saving of $67,748
• 15 years instead of 30: total interest $155,683, a saving of $191,832, but the payment rises to $2,532
• $200 extra toward the balance each month: total interest $256,341, a saving of $91,174, and the loan ends almost seven years early

The Mortgage Calculator puts these scenarios next to each other, which is easier than running the same loan three times.

Extra payments work best early, and only if they hit the balance

An extra $200 in month one takes $200 off a balance that would otherwise have carried interest for 29 more years. The same $200 in year 25 saves a fraction of that. The return on an extra payment is your loan rate, guaranteed, and it is highest at the start.

Three ways people do it:

A thirteenth payment a year. Paying every two weeks, half a payment each time, gives 26 half payments, which is 13 full ones. On the $300,000 loan that one extra payment a year saves about $73,700 in interest and finishes the loan about five years early.

A lump sum. A bonus or a tax refund put on the balance. $5,000 in month twelve of that loan saves about $22,400 in interest over its life.

Rounding up. $1,799 becomes $1,800 or $2,000. Small, but it runs for 360 months.

Check where the money lands. Some lenders book an extra payment as an advance on next month instead of a reduction of the balance. That saves you nothing. Say "apply to principal" in writing, then check the next statement. In the Netherlands most lenders let you repay 10 to 20 percent of the original loan per year without a penalty; above that a fee can apply during a fixed-rate period, so read the mortgage terms before a large lump sum.

The Loan Calculator has an extra payment field. Put your own loan in and try $50, $100 and $200 to watch the payoff date move.

Fixed rate, variable rate, and the Dutch fixed period

A fixed-rate loan has one rate and one payment for the whole term. The schedule is known on day one.

A variable-rate loan resets the rate on a timetable, usually against a benchmark. The schedule is then a projection at today's rate. When the rate changes, the remaining balance is re-amortized over the remaining months at the new rate, and the payment moves with it. A loan that starts at 4.5 percent and resets to 6.5 percent costs more per month and far more in total.

US mortgages often mix the two: a 5/1 ARM (adjustable-rate mortgage) is fixed for five years, then adjusts every year. Dutch mortgages work with a rentevaste periode (the fixed-rate period), commonly 10, 20 or 30 years, after which you pick a new fixed period at the rate of that day. Different names, same mechanic: the schedule is only certain for as long as the rate is.

To model it, run the calculator once for the fixed period, take the balance at the end of it, and run it again from that balance at the rate you fear. If the second run still fits your budget, the variable option is affordable. If it does not, the lower starting rate is a bet, and you should know that you are placing one.

Compare offers on interest over the years you will keep the loan

The interest rate alone does not settle which offer is cheaper.

APR includes the fees. A 5.5 percent rate with $8,000 in fees and a 5.75 percent rate with $2,000 in fees are closer than they look. APR spreads the fees over the term, which is fair if you keep the loan to the end and misleading if you sell in year eight.

Shorter term, higher payment, far less interest. A 15-year loan beats a 30-year loan on total cost every time. A 30-year loan plus voluntary extra payments gets close to the same result while keeping the option to pay less in a bad month. I prefer that flexibility. You may not.

Count the years you will actually keep it. Build the schedule for each offer and compare the interest paid up to the month you expect to sell or refinance, not the full term. Most people do not keep a 30-year loan for 30 years.

The Investment Calculator answers the follow-up question: take the lower payment and invest the difference? If the loan is at 5 percent and the investment returns 8 percent, the math favours investing. The loan interest is certain and the investment return is not, so that is a question about your appetite for risk, not about arithmetic.

FAQ

Why does the interest share fall over time?

Because it is charged on the remaining balance, and the balance falls with every payment. The payment stays the same, so as the interest share shrinks the repayment share grows.

Can I repay early without a penalty?

Depends on the contract. Many consumer loans and US mortgages allow it. Dutch mortgages usually allow 10 to 20 percent of the original loan per year free of penalty, and charge a fee above that during a fixed-rate period. Read the terms or ask the lender before you send the money.

What is negative amortization?

A payment that does not even cover the interest. The shortfall is added to the balance, so you owe more after paying than before. It shows up in some adjustable mortgages, payment-option loans and income-driven student loan plans. Avoid it unless you know exactly why you are in it.

What does refinancing do to the schedule?

It starts a new one. Refinance a 30-year loan after ten years into another 30-year loan and you are back in the interest-heavy early months. That is why refinancing pays off when the new rate is a lot lower, not slightly lower, and only after the fees are counted against the years you will keep the new loan.