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Compound Interest - The Formula
So, how can we figure out compound interest without having to go through each little step?

We'll use something called the "growth factor" of money.

Let's just do a problem and you'll see what I mean:

If we invest $1.00 in an account that pays 12% compounded quarterly, how much will we have in the account at the end of one year?

initial amount invested = $1.00

At the end of each period (quarter), we'll be earning 3%...
So, each $1.00 will turn into $1.03...
growth factor = $1.03

number of periods = 4

Here's the formula:

So, with our numbers...

Hey, it works!  We got the same amount that we got doing it the long way... And this way was a LOT easier.

Let's try something a little messier:

If we invest $20,000 in an account that pays 8% compounded semi-annually, how much will be in the account in 15 years?

initial amount invested = $20,000

At the end of each period (six months), we'll be earning 4%...
So, each $1.00 will turn into $1.04...
growth factor = $1.04

number of periods = 30
(That's twice a year for 15 years)


(I rounded it to two decimal places since it's money.)

Let's get some bigger bucks flowing here...

If we invest $60,000 in an account that pays 9% compounded semi-annually, how much will we have in the account in 25 years?

initial amount invested = $60,000

At the end of each period (six months), we'll be earning 4.5%...
So, each $1.00 will turn into $1.045...
growth factor = $1.045

number of periods = 50

What if we make the same investment, but compound it quarterly?

initial amount invested = $60,000

At the end of each period (every 3 months), we'll be earning 2.25%...
(  That's 9% divided by 4 ----   .09 / 4 = .0225  )
So, each $1.00 will turn into $1.0225...
growth factor = $1.0225

number of periods = 100

See how we made more money?  Will we make even more if we compound it monthly?

initial amount invested = $60,000

At the end of each period (every month), we'll be earning 0.75%...
(  That's 9% divided by 12 ----   .09 / 12 = .0075  )
So, each $1.00 will turn into $1.0075...
growth factor = $1.0075

number of periods = 300

So, the more time we compound, the more money we make!!  Cool.
 

Most standard savings accounts compound quarterly...  But, some investments, like certificates of deposit (CDs) DO compound monthly.

But, there's one trick to this...  Banks can compound as often (or not often) as they like and they won't tell you how they're doing it -- UNLESS YOU ASK!  It won't make a lot of difference unless you have a big chunk of money...  But, check out these numbers: 

Invest $1000 at 3% compounded yearly (just once a year) for 10 years...  You'll have $1343.92.

Invest $1000 at a lower rate, 2.98%, compounded monthly for 10 years... You'll get more interest and have $1346.66.  Sure, it's only a few bucks, but every penny counts in the long run!

Check out the same investments with some big bucks for a longer time:

Invest $100,000 at 3% compounded yearly for 45 years...  You'll have $378,159.58.

Invest $100,000 at 2.98% compounded monthly for 45 years...  You'll have $381,651.45.

The difference is $3491.87 and that'll buy something fun!
 

Banking, etc.

The Math of Money

Owing Money

Credit Ratings

Investing

Be Smart & Rich

Calculators

 

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