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# What Is Compounding?

## What Is Compounding?

Compounding is the process in which an asset’s earnings, from either capital gains or interest, are reinvested to generate additional earnings over time. This growth, calculated using exponential functions, occurs because the investment will generate earnings from both its initial principal and the accumulated earnings from preceding periods.

Compounding, therefore, differs from linear growth, where only the principal earns interest each period.

### Key Takeaways

• Compounding is the process whereby interest is credited to an existing principal amount as well as to interest already paid.
• Compounding thus can be construed as interest on interest—the effect of which is to magnify returns to interest over time, the so-called “miracle of compounding.”
• When banks or financial institutions credit compound interest, they will use a compounding period such as annual, monthly, or daily.
• Compounding may occur on investment in which savings grow more quickly or on debt where the amount owed may grow even if payments are being made.
• Compounding naturally occurs in savings accounts; some investments that yield dividends may also benefit from compounding.

## Understanding Compounding

Compounding typically refers to the increasing value of an asset due to the interest earned on both a principal and accumulated interest. This phenomenon, which is a direct realization of the time value of money (TMV) concept, is also known as compound interest.

Compounding is crucial in finance, and the gains attributable to its effects are the motivation behind many investing strategies. For example, many corporations offer dividend reinvestment plans (DRIPs) that allow investors to reinvest their cash dividends to purchase additional shares of stock. Reinvesting in more of these dividend-paying shares compounds investor returns because the increased number of shares will consistently increase future income from dividend payouts, assuming steady dividends.

Investing in dividend growth stocks on top of reinvesting dividends adds another layer of compounding to this strategy that some investors refer to as double compounding. In this case, not only are dividends being reinvested to buy more shares, but these dividend growth stocks are also increasing their per-share payouts.

## Formula for Compound Interest

The formula for the future value (FV) of a current asset relies on the concept of compound interest. It takes into account the present value of an asset, the annual interest rate, the frequency of compounding (or the number of compounding periods) per year, and the total number of years. The generalized formula for compound interest is:



F

V

=

P

V

×

(

1

+

i

)

n

where:

F

V

=

Future value

P

V

=

Present value

i

=

Annual interest rate

n

=

Number of compounding periods per year

begin{aligned}&FV=PVtimes(1+i)^n\&textbf{where:}\&FV=text{Future value}\&PV=text{Present value}\&i=text{Annual interest rate}\&n=text{Number of compounding periods per year}end{aligned}

FV=PV×(1+i)nwhere:FV=Future valuePV=Present valuei=Annual interest raten=Number of compounding periods per year

This formula assumes that no additional changes outside of interest are made to the original principal balance.

### 536,870,912

Curious what 100% daily compounding looks like? One Grain of Rice, the folktale by Demi, is centered around a reward where a single grain of rice is awarded on the first day and the number of grains of rice awarded each day is doubled over 30 days. At the end of the month, over 536 million grains of rice would be awarded on the last day.

## Increased Compounding Periods

The effects of compounding strengthen as the frequency of compounding increases. Assume a one-year time period. The more compounding periods throughout this one year, the higher the future value of the investment, so naturally, two compounding periods per year are better than one, and four compounding periods per year are better than two.