Compound Interest: The Silent Killer

I bought my first house about three years ago. It was my second major purchase (the first being a minivan, so I suppose this was an upgrade), so I was no stranger to the confusing and mind-numbing paperwork involved. But, while a car purchase usually requires a financing agreement, a vehicle inspection report, and proof of insurance, I believe that they had to chop down two or three trees in order to handle all of the paperwork involved in buying a house.

Somewhere in the midst of that avalanche of affidavits and agreements is your mortgage: a piece of paper from a bank that says "we'll loan you much more money than you make in a year, and you can pay us back a little bit at a time, with interest."

You don't need accounting classes to understand the basic concept of interest. Let's say you get a $1000 loan with 10% interest, that you pay back over 12 months. In it's simplest (and least profitable) form, that means you actually pay $1100 (10% of 1000 = 100) over those 12 months, or about $92 a month. Since this is a one year loan, you would say that the interest is "compounded" annually.

So what is "compounded" interest? The qualifier -- annually, monthly, daily -- tells you how often they put interest on the "principal": the remaining amount of money you owe on the loan.

Mortgages and credit cards generally have agreements to compound interest monthly. The generous lenders will compound quarterly. And now's the time to break out the calculator.

There's a mind-numbingly tedious way to determine total interest, and then there's the math way (which I like to call the "fun" way):

Let's say you got a 30 year mortgage for $150,000 and a 4.5% fixed rate interest (compounded monthly). First, how much would you pay over 30 years if the interest was zero?

$150,000/360 months = $416.67

Then, we need a magical formula for determining how to add the interest:

I = Fixed Rate (4.5%)
T = Term in Years (30)
A = I * T = 0.045 * 30 = 1.35
B = 1/2*Y = 0.675 (this is for simplification purposes)

The formula your lender uses to determine your monthly payment looks confusing, but we'll walk through it:

Monthly Payment = Zero Interest Payment * (1 + B + B²/3)

This is, actually, an approximate formula based off of what is actually a series:



where L is the principal, P is the payment, n is the number of months, and i is the annual interest rate compounded monthly. Between my formula and the "official" formula, which would you rather use?

I thought so.

So let's plug in our numbers on my formula:

Monthly Payment = $416.67*(1 + 0.675 + (0.675²)/3)
Monthly Payment = $416.67*(1.675 + 0.151875)
Monthly Payment = $416.67*(1.826875)
Monthly Payment = $761.20

Wowza. So for $150,000 house you actually give the lender nearly $275,000 over the life of the contract. Lenders know that people rarely have $100,000 saved up in their banks. They also know that people rarely stay in the same house for 30 years, either selling it, or foreclosing on it. With the compounded interest the banks mitigate their risk, taking a large chunk of the interest out early on.

So how does a homeowner fight back from this? Simple: pay as much as you can towards the principal each and every month. If you can afford an extra $100, then add $100. If you get a hefty tax return, then add that. Every single dollar you take off of the principal equates to almost $2 savings in interest. That can really add up over time.