# Mortgage vs. Loan?

I understand the math behind how banks calculate the interest to principal ratio throughout the amortization period. I want to know why banks want you to pay as much interest as possible first? In a normal loan, when I make a payment, if the interest is 10% of the total amount, 10% of the payment will go to interest, the rest to principal. Is a "mortgage" just a fancy name for a warped version of a loan where you have to pay more or am I mistaken? Thanks for any insight.

• It's a simple factor of time. The interest calculated every period is based on the amount left on the loan. Earlier in the loan, you have a higher balance that is accruing interest. Later on, it's lower. This applies to most student loans, car loans, mortgages, etc. Anything with a flat monthly payment works out this way, because math. – Noah Mar 23 '15 at 16:52
• @MarkusHallcyon Noah's comment is perfectly correct, and does indeed answer your question -- there is no need to be so rude. Perhaps you don't understand what interest means? 10% interest means that 10% of the principal amount is owed as interest (in addition to the principal), not (as you seem to think) that 10% of your payment is suppose to be going towards interest and 90% towards the amount due. – Dilip Sarwate Mar 23 '15 at 20:16
• Are you sure your understanding of normal loans is correct? – JB King Mar 23 '15 at 20:22
• The only thing I can think of, is that the understanding expressed in the question sounds almost like payday type loans - where the "interest" is just an up front fee. – Joe Mar 23 '15 at 20:25
• @MarkusHallcyon, I believe you are mistaken. The interest gets added onto the principal and then your payment comes off. If your loan is for \$1000 and interest is 10% or \$100, then the loan amount will increase to \$1100. Then if your repayment is \$110, the loan balance will move to \$990. If you make extra repayment, say \$200 instead of \$110, then your loan balance will move to \$900. – user9822 Mar 23 '15 at 20:45

Here is a simple example based on Joe's discussion in comments.

Suppose that for a given month you owe \$50 of interest. Let's say you make a \$100 payment.

If all of this money goes to the principal, you reduce the principal by \$100. But you did not pay the \$50 interest, so it gets added to the principal. This means you reduced the principal by \$100 but then increased it by \$50, for a net decrease of \$50.

Suppose that instead you pay the \$50 of interest and then use the extra \$50 to pay down the principal. You have only paid \$50 toward the principal, but since you paid the interest, it wasn't added to the principal, so again the net decrease in principal was \$50.

In both cases you reduced the principal by \$50. You cannot reduce the principal more by stipulating that you want all of your payment to go to the principal, because if you don't pay the interest, it will be added to your principal, canceling out the extra you paid.

• Okay this makes sense, I was confused about how exactly the interest was calculated. – Markus Hallcyon Mar 23 '15 at 21:13
• @MarkusHallcyon - in which case, with all due respect, the first sentence of your question is misleading. You don't understand the math behind how banks calculate the interest to principal ratio throughout the amortization period. It's fine to come here and try to understand the process. But you don't disclose your current level of non-understanding. – JoeTaxpayer Mar 23 '15 at 23:45

The way the loan is structured, "duration to payoff" is the basic factor that determines the total loan payment per month, along with a general desire to have a stable mortgage payment (ie, the same payment every month). This drives the small amount going to principal (not the large amount going to interest).

At any given time, for a particular month, you accumulate \$I in interest. This amount will be due regardless of how much principal you pay off with the payment: you have a \$100,000 balance loan (right now) at a monthly equivalent interest rate of 0.5% for simplicity; so you owe 0.5%*100,000 (or \$500) in interest for the month. That's how interest works - it depends on the current value of the loan. (This is usually compound interest compounded daily, so it's more complicated than this, but it's about the same idea.)

Your total payment will be \$I + \$P. \$P is where the 15 year, 30 year, etc. comes into play. When you pay some principal this month, say \$100, you will have a smaller interest payment next month, right? \$99900 * 0.5 is now \$499.50. So, if you keep a \$600 flat monthly payment, you will now only owe \$499.50 in interest and pay off \$100.50 in principal. The next month you pay \$499 in interest and \$101 in principal... etc. Eventually your principal will be \$500 and your interest will be \$100, because your total loan balance will be only \$20000. So over time, \$I+\$P=payment, and I goes down while P goes up simply due to the math on the interest owed for that period. You're not paying interest for future months or anything like that in your payment (normally); you're just paying more interest now because you owe more now on the amount you've got outstanding.

The exact amount of total payment, and thus the exact amount of principal you pay with the first few payments, depends on the mortgage term. Paying \$700 total (so starting at \$200 a month principal) clearly has a lower amount of total payments than \$600 a month. The mortgage company sets the payments up based on a formula that determines you will have exactly 360 equal payments (30 years), or 180 equal payments (15 years), or whatever schedule you prefer. The equal payments is assumed to be in your interest (to have a stable monthly bill) - but you're (usually) permitted to pay more principal at any time if you prefer.

This is only applicable to fixed rate mortgages; variable rate mortgages may not have constant payments (or may have longer or shorter terms based on the variability of interest).

I recommend you find a mortgage calculator, figure out a payment schedule, then plug it into excel - see the amount of P+I in the first month, then calculate how much I should be in the second month, how much P, etc., all the way down to 360 payments (or whatever your loan term is). I did this once and it made this whole bit make a lot more sense to me.

• Because you have to pay the amount of interest due each month. If you owe \$500 in interest in the first month, you can't just pay \$100 and say "I only want \$10 to go to interest" - where would the other \$490 of interest go? – Joe Mar 23 '15 at 17:34
• The amount of interest due isn't some arbitrary amount a bank feels like assigning. It's the rate you agreed on (say an APR of 6% for convenience), then accumulated over the month at a daily rate, which works out to something close to 0.5% (6%/12) per month. That month you owe 0.5% of your present loan balance as interest, every month. You have to pay that before you pay any principal, but that's really an arbitrary distinction; you add 0.5% to your principal for interest every month, then you have to pay it off plus some more so your mortgage isn't getting bigger. – Joe Mar 23 '15 at 17:36
• The interest for that payment has nothing at all to do with the principal for that payment. The interest for that payment is solely determined by the principal amount now (well, over the course of the past month). The interest payment amount is not based on the length of the loan. The principal payment amount is based on the length of the loan. – Joe Mar 23 '15 at 17:42
• You still have to pay the interest, though. When are you planning to pay that? Your mistake is in thinking the interest is some other amount that's unrelated to the principal. Think of it as if the interest is being added each month to your principal; then all of your payment is going to principal. The interest for your current payment is based on the current due - not the length of the loan. Of course you're welcome to pay more principal and reduce interest (usually) - that's a great idea. But it doesn't reduce your now interest. – Joe Mar 23 '15 at 17:52
• @MarkusHallcyon: If you owe the bank \$500 interest, then you can tell them all day long that you are paying the principal only, but that means the \$500 interest that you owe will be added to the principal. – gnasher729 Mar 24 '15 at 0:25

One way to perhaps reduce the confusion is to realize that there is no distinction between principal and interest.

Say you borrow \$100,000 and agree to pay it off with equal monthly payments over 20 years, while paying interest at 12% a year, compounded monthly (or 1% a month).

So you walk out with \$100,000, and the mortgage company sets up a leger page or a file or a spreadsheet or whatever...

One month later, a timer clicks over, and the company sees that you've owed them \$100K for a month, so they charge you \$1000 interest (1% of \$100,000). So they just kick up the amount owed by that amount, so you now owe \$101,000. There is no separate interest account; there's just a new, higher amount owed.

Luckily, the same day, \$1101.09 arrives from you. The mortgage company updates their records again, credits all your payment against the new balance owed, and winds up the day with you owing them only \$99,898.91

One month later, the timer kicks over again, and they assess you \$998.99 in interest (still 1% of that month's balance). The same day, your second payment of the same \$1101.09 arrives, so when the dust settles, your balance owing is \$99,796.81

Why \$1101.09? Well, there are ways to calculate that if you follow the above process 240 times, the 240th payment of \$1101.09 will reduce the balance owed to exactly zero. Here is an amortization schedule showing the first 19 payments on this example. Note that the payment is always the same, and that the interest in any month is just 1% of the previous month's balance. Missing a payment, making an extra large payment, changing the interest rate can all mess things up...

PS: There are tax reasons in some jurisdictions to know how much interest you've paid...

In order to maintain a constant payment over the life of the loan, the relative percentages going to interest and principal change over time. Most loans (check with your bank) will let you make additional payments against principal, which will have the obvious effects in terms of reducing total interest paid and time to pay off.

Each month you owe interest on your entire loan balance.

If you borrow \$100,000 at 12%/year then your monthly interest rate would be 1% (12%/12 months). Lets assume this is a 10 year mortgage for the math below.

That means that each month you pay 1% interest.

The first month, you'll owe and pay \$1000 interest (1% of borrowed money).

Because we value having level, equal payments we amortize the principal so that the monthly payment is the same. A quick calculator shows the payment is \$1435 so \$1000 to interest and \$435 to principal to start for the first payment where the interest amount will gradually decrease and the principal amount will gradually increase.

What if we paid the principal equally each month?
We would pay off the principal at the rate of \$100,000/120 months or \$833/month.

Your very first mortgage payment would be \$1833. Your very last mortgage payment would be \$841 (\$833 principal + 1% interest of \$833 principal).

Both pay the appropriate amount of interest and principal and pay off the loan in 10 years. Amortized gives you a payment that is Fixed but the ratio of principal to interest changes and a fixed principal amount gives you a different mortgage payment each month.

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