Automagical Principles: Compound Interest

Today we’re going to talk about compound interest.

It occurs to me that many of didn’t take an extensive amount of financial-type classes in high school or college, so for the ones of you who did, bear with me… it’s to the shame of America’s high schools this isn’t taught as required cousework.

The Time Value of Money

First, a tutorial on the time value of money…basically, money is never more useful than it is right this moment. If I want to buy something, and I want it right now, you loaning me the money tomorrow or next year is going to be worth less to me, because I have to sit around and wait. If it’s a business opportunity I’m waiting on, I could be missing out on a major chance for making some cash.

So, in an effort to quantify this fact that money is worth so much more to me now than a year from now, interest rates exist to put a definitive value on the difference in value of a dollar loaned right now, versus a dollar loaned a year from now.

Interest: One Year

A year?, you may say.. what could possibly happen in a year… how could my dollar possibly be worth alot more than it is now a year from now? And you’re right. It’s not much. In fact, given the current yield (another word for rate of return/interest rate) on one-year CD’s (certificate of deposit, a generally safe loan to a bank, which allows them usage to your money for the term [in this case 1 yr], at which the end of they pay you back the original amount plus interest)… if you invested $5 in a CD [at 5%] right now, they’d pay you back $5.25 a year from now.

25 cents?! a quarter?! Big blippin deal.

Compound Interest

That’s where the automagical part comes in. You see, over a year, this is no big deal. It’s easy to calculate, it’s definitely not alot of money. But alot of you are young, most of you are under the age of 30. Which means you have a long time (20 to 40 years, depending on circumstances) before any major expenditures for college for children or retirement for yourselves.

Compound interest works by taking your 5$, investing it over a long time frame, and re-investing all proceeds from each year or month’s interest back in to that original $5 (called the principal). So, given the above example, if you invested 5$, allowing it to compound for 30 years instead of one, at 8% rate of return (yeah, it’s higher. It’s also a realistic average over a 40 year time frame, assuming the world doesn’t fall apart), re-investing the interest back in to the investment each money you’d have…

$54.68 in the year 2036. If you let it sit till 2046 (40 years), it’d be $121.37.

A Practical Approach

Let’s try something alittle more practical. Let’s pretend we’re talking your retirement savings, and you invest 150$ each month for you and your spouse in to some form of retirement account, let’s say a Roth IRA to keep taxes out of this (a Roth IRA is not taxed when you pull the money out in retirement). You, being 25, expect to work till around 65, and will contribute a total of 300 a month, or 3600 a year for your family till that age.

Let’s also consider inflation averaging around 3%, and you’ll earn a return of 9%, because you’re leet. This leaves us with an adjusted return of 6%.

Principal: 0
Annual Addition: 3600
Years to grow: 40
Interest rate: 6%
Compound interest: 12 times(s) annually.

Future amount, in 2046: $600,434.46. (keep in mind, since the interest rate was adjusted for inflation, that means that 600k would buy exactly the same amount of stuff that 600k would buy right now.)

If we bump the interest rate to 7%, you’ve got 792,000, up to 8%, 1,054,000, 9%… 1,415,000.

Expontential Wierdness

The blessing and curse of compound interest is that its expontential. Small changes in the interest rate (going from 6% to 9%, only 3%, or a 50% increase) resulted in a massive difference of $814,566 (600,434 -> 1,415,000, a percentage increase of 135%!!1). If you wanted to have 1,415,000 at the end of 40 years at 6% return, you’d have to change your original investment of $300/month (3600$ annually) up to $708.33/month ($8500 annually). Crap.

Summary

1. Every month (or year, or day, whatever timeframe you like) saving is delayed results in a massive difference of the final sum, way more than it would seem due to the exponentiality of compound interest.

2. Because of #1, setting realistic goals and budgetting appropriately for long-term savings is a high priority.

3. While this post may seem to be based in greed and how to get lots and lots of money, temper everything you see here with this post.

FL: How To (actually) Dismantle an Atomic Bomb - step-by-step instructions, with pictures!!1 Provided courtesy of Jason.