# The Beauty of Compounding

If you put \$1,000 into a savings account at 2% annual interest, at the end of two years, your balance won’t be \$1,040 (\$1,000 principal + \$200 interest each year). You will have a little more than that.

At the end of Year 1, you will have earned \$20 interest for an ending balance of \$1,020. Therefore, in Year 2 you earn 2% interest on \$1,020, not only \$1,000. That is the beauty of compounding: you earn interest on both the original principal and previously earned interest that’s added to the principal balance. As a result, you end up with \$1,040.40.

## Compounding Frequency Matters

The above example would be accurate if the bank only compounds (added the interest to the principal) interest once per year. In practice, banks usually compound interest at shorter intervals, usually on a daily, monthly, or quarterly basis.

The more frequently the bank compounds interest, the better for you. The more frequently you are credited for the interest, the higher your annual percentage yield (APY), the effective rate of return for the year.

If your bank compounds interest daily, the bank credits your account with 1/365 of the interest rate every day. In this case, the compounding increases the value of your account every day.

If your bank compounds interest quarterly, the bank credits your account with 1/4 of the interest rate every quarter. The compounding increases the value of your account every quarter.

## A Concrete Example

Let’s calculate how the APY changes when a bank that pays 2% annual interest rate compounds every day versus every quarter:

The APY formula is (1 + R/N)N – 1. R is the interest rate and N is the number of compounding periods per year.

So for Bank A, the APY is calculated as (1 + 0.02/4)4 – 1. For Bank B, it is (1 + 0.02/365)365 – 1.

Bank A’s APY is 2.015% and Bank B’s APY is 2.02%.

The difference is small, but it’s still a difference. If the interest rate were higher, the difference caused by compounding would be larger.

## Stock Investing and Compounding

Compounding comes into play in stock investing as well.

One example would be dividend reinvestment. If you reinvested in a publicly traded company’s DRIP (dividend reinvestment plan), every time the company pays a dividend, the dividend would automatically be used to purchase additional shares of that company’s stock commission-free.

Over time, because you will have more and more shares of the stock, you receive more cash dividend, which then would purchase more shares, and when the stock price rises, in dollar terms you also gain more. It becomes a virtuous cycle.

To illustrate the compounding effect of DRIP, let’s consider a hypothetical example.

## How DRIP Can Turn Into Profit Pool

Let’s say 10 years ago you invested \$5,000 in 100 shares of XYZ stock. XYZ pays \$3 per share in dividend annually. The dividend doesn’t grow, but the stock price grows at an annual rate of 5%. At the end of 10 years how big a difference would DRIP make?

If you participated in XYZ’s DRIP, at the end of 10 years that \$50,000 would have turned into \$12,807, and you would own 157.26 shares of XYZ.

If instead you just kept the dividend in cash, your total investment, including the dividend received, would be worth \$11,144, or 13% lower than the DRIP scenario. Of course, if you were able to invest the cash dividend in something that has an even greater return, you could beat the return of the DRIP scenario, but that’s a big if.

A word of caution: if XYZ falls in price, the compounding effect of DRIP could increase the size of the loss. However, since historically stocks rise in value, the net compounding effect of DRIP will very likely be positive.

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