# What is Compound Interest?

Compound interest is interest calculated on the principal amount invested, which is then added to the principal amount, and compounded again. It can be earned daily, weekly, monthly or yearly. Generally, the more times an amount is compounded, the more money a person can make.

As long as a person leaves an interest earning account alone, by not removing money from it, he begins making more money on the investment (given a stable interest rate) because the money he earns is added back to the principle amount. It’s a simple fact that more money earning interest makes more money. Each time interest is compounded, the money earned gets added to the total.

A similar result can be seen by someone raising rabbits. If two bunnies produced a litter, and the person kept all those bunnies, then he might end up with eight rabbits. The original bunnies would keep on breeding, as would the new litter, and more and more rabbits would be produced. Compound interest won’t be quite that dramatic, unless the person is investing huge sums of money. The important parallel is that the first pair of bunnies (the original investment) and their offspring (interest) now combine together to produce yet more rabbits, and as combined, they will produce a great deal more than if they were sold off and separated.

Most investment firms, banks, and the like will state how often interest is compounded in an account. In some cases, the investment doesn’t compound, but earns what is called simple interest. This means that the investor only makes money on the amount he initially invested, and the profits are not reinvested to make more money.

Individuals can figure out exactly how much an investment will be worth in a few years with a scientific calculator. They also need to know the initial investment amount (principal or p), the rate of interest, (r), the number of years they plan to allow the investment to sit (years or y), and the number of times per year the investment will compound (t). Investors should remember that only a portion of the interest would be earned each month, so the interest amount would have to be divided by the total times interest gets compounded each year (t). The formula is as follows:

**Total value = p(1 + r/t) ^{ty}**

Putting this to work, in dollar amounts, someone might invest $10,000 US Dollars (USD) in a savings account that earns 5% interest per year and is compounded monthly. If the person leaves that money alone for five years, he could figure out exactly how much money he’d make in that time period, and the value of the account at the end of four years. The equation would look like this:

**10,000(1 + 0.05/12) ^{12 X 5} = $12,833.59 **

If the investor only earned simple interest, at even 5.5% per year, he wouldn’t make that much money:

** 10,000(1 + .055 X 5) = $12,750.00**

One reason to understand compound interest is because some accounts that earn simple interest offer a higher yearly interest rate. If the investment is long term, however, the investor may make more money with a lower interest rate that compounds. On the other hand, if an investor knows that he’ll be removing the money after a year or two, a higher interest rate that is not compounded may be a better investment, than an account that compounds the interest but has a lower rate. Investors also shouldn't be daunted by these formulas; anyone who has access to the Internet can find hundreds of sites that offer interest calculators, and most of them are very easy to use.

## Discussion Comments

Could someone explain if compound interest is magnified with a larger base sum?

Which is the greater yield over 20 years: $10,000 in one account with interest of 5 percent or

£5,000 in two separate accounts, still at 5 percent?

Most financial equations can be done with a financial calculator or an online mortgage calculator, but it is nice to see that people still work the problems out long hand. I would like to ask if the formula is still the same when the interest compounds more than once a year? Could someone show me a formula that takes this into account? I wish learning financial math was mandatory when I was in high school.

Understanding compounding interest is also helpful in planning for a large purchase, or for retirement. Let’s say that I needed $40,000 for a down payment on a house in five years. Assume that I know of an investment vehicle that will return 11% per year, and I wanted to determine how much I would have to invest today so that I could walk away with $40,000 when the investment matures. To determine the present value of $40,000 I would use the following equation PV=FV[1/(1+i)^n]. (PV=Present Value, FV=Future Value, i=interest, and n=number of years). The equation would look like this: 40,000[1/(1+.05)^5]=31,341.05. I would have to put $31,341.05 into the investment to make an ROI of $40,000.

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