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Compound Interest Formula and Examples

Compound Interest Formula and Examples

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One of the most powerful forces in finances is compound interest. Compound interest is interest that is paid on the principal and also on the interest that previously earned on your investment. This helps you grow your investment at an accelerated rate. On the other hand, compound interest can work against you — for instance, as finance charges against your credit card debt that could quickly snowball out of control. It can be a great burden or a great boon. It all depends on the money choices you make.

Compound Interest Examples

Compound interest means that the interest you earned from the previous period is added to your balance, and you are now earning interest on the new total.

Example #1 – Simple Yearly Compounding

You deposit $10,000 into an account with a 5% yield paid annually. At the end of the year, your $10,000 earned $500, which is added to your account now totaling $10,500.

At the end of Year 2, your $10,500 earned $525 interest — $500 from your original $10,000 and $25 from the $500 interest you earned the first year. That is compound interest.

Compound Interest Formula and Examples 1

 

Here is another look in a table format:

Compound Interest Formula and Examples 2

Example #2 – Daily Compounding

In real life, compounding usually happens daily. This means your money earns 1/365 of the interest rate each day, and the interest is added to your account daily.

Here’s the compound interest formula:

Compound Interest Formula and Examples 3

Here are the variables:

  • SB = $10,000 starting balance
  • r = 5% interest rate
  • n = 365 for daily compounding
  • nt = 365 days

Solving for Ending Balance:

  • EB = $10,000 ( 1 + 5% ÷ 365)^365
  • EB = $10,512.67

In the example above, 5% compounded daily would result in $512.67 interest earned after one full year.

Example #3

Let’s go back and use this formula on example #1 with the following variables

  • SB = $10,000 starting balance
  • r = 5% interest rate
  • n = 1 yearly compounding
  • nt = 3 years

Solving for Ending Balance:

  • EB = $10,000 (1 + 5% ÷ 1)^3
  • EB = $11,576.25

Annual Percentage Yield (APY)

Annual Percentage Yield is the total interest you earn, including compound interest. This assumes that you deposit into your account once, keep the fund for the entire year, and do not make any deposit or withdrawal.

For example, if an account has an interest rate of 5%. The APY would be 5.1267% (as per Example #2).

Making Compound Interest Works for You

Compound interest can be a great gift to you if you avoid debt and get into the habit of saving and investing your money.

A high yield savings account can get you a 2.4% annual yield or higher, but the real money is made investing in the Stock Market, where the average yearly return in about 9%.

When you put money into interest-bearing accounts or dividend-yielding investments, you get paid for letting your money sit there. For example, if you have $1,000 and an average 5.00% APY across your savings and investments, after a year, you’ll earn $50 in interest and dividend. If you let your money sit in your savings account and reinvest the dividend, the following year you will earn $52.50 — doesn’t sound like much, but your original $1,000 will turn into $1,628.89 after 10 years, $2,653.30 after 20, and $4,321.94 after 30!

Tips for Making Compound Interest Works for You

  • Start immediately to save and invest your money. The earlier you start, the more you will earn as compound interest works on your behalf. How much you start with isn’t as important as getting started.
  • Let the money sit. This is easiest in a retirement account. Leave the money alone. It will gradually build upon itself as the interest you earn is added to the principal amount you invested — and then interest is earned on the new total.
  • Add new money to your account regularly. While compound interest works well, you can multiply the power of compound interest by making regular additions to your savings and investment accounts.

Compound Interest Can Work Against You

One of the most destructive examples of how compound interest can work against you is credit card debt.

Every month your interest charges are added up and then tacked on to the balance. Pretty soon, you are paying interest on your interest and barely reducing the principal at all — especially, if you only pay the minimum. In fact, it is possible to pay back many times what you originally borrowed when you are only paying the minimum.

Other loans charge compound interest as well, but credit card debt is the most devious. It can also be one of the most difficult to get out of, since the interest rates charged are so high, and in some cases, the interest is compounded daily.

Consider your financial choices carefully. You want to be making compound interest work for you, rather than working against you.

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Spivey
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Good Overview. Compound interest is one of the most important concepts when trying to develop financial freedom. You had a good example in the second section showing how your money can grow using it. If you ever re-post this article you may consider showing an example where you continue to add to the investment as well as the involvement of compound interest, then contrast the two.

Alex
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Alex

Good basic description of compound interest and how it can work for and against you. To really attract people to start saving early, i would go with an example of saving say 10% of your paycheck every time, over 20 years, with the compounded interest. It is really amazing to look at what can happen if you start saving early, and keep saving. remember that the 10% gets higher as you get promotions and raises over your entire career. One of the most interesting savings strategy’s i have been introduced to is to act like you smoke cigarretes. save 1… Read more »

Compound Interest Formula and Examples

by Pinyo Bhulipongsanon time to read: 3 min
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