When it comes to calculating interest, there are two basic choices -- simple and compound. Simple interest simply means a set percentage of the principal every year, and is rarely used in practice.
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On the other hand, compound interest is applied to both loans and deposit accounts. Compound interest essentially means "interest on the interest" and is the reason many investors are so successful.
Comparing simple and compound interestLet's say you invest $10,000 at 8% simple interest. This means that after the first year, $800 is added to your account. In the second year, another $800 in interest is paid, and the same with the third year, fourth year, and so on.
If your investment paid 8% compound interest on an annual basis, it wouldn't make a difference at first. After the first year, you'd receive the same $800 interest payment as you would with a simple interest calculation. However, this is where it starts to get very different.
In the second year, your 8% interest is calculated on your entire new balance of $10,800, not just your original $10,000. This produces an interest payment of $864 for the second year, which is then tacked on to the principal when calculating your interest for the third year.
You may be surprised at how quickly this can add up. At 8% simple interest, your $10,000 investment would be worth $34,000 after 30 years. However, using compound interest, the value would balloon to more than $100,000. Just take a look at how simple and compound interest compare over a 50-year period:
Compounding frequency makes a differenceIn the previous example, we used annual compounding -- meaning that interest is calculated once per year. In practice, compound interest is often calculated more frequently. Common compounding intervals are quarterly, monthly, and daily, but there are many other possible intervals that can be used.
The compounding frequency makes a difference -- specifically, more frequent compounding leads to faster growth. For example, here is the growth of $10,000 at 8% interest compounded at several different frequencies:
The compound interest formula and an exampleTo calculate compound interest over time, there is a mathematical formula that you can use:
Where "A" is the final amount, "P" is the principal, "r" is the interest rate, expressed as a decimal, "n" is the number of compounding periods per year, and "t" is the time period in years.
For example, let's say that you're investing $20,000 at 5% interest, compounded quarterly, for 20 years. In this case, "n" would be four, since quarterly compounding occurs four times per year. From this information, we can calculate the investment's final value after 20 years like this:
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