What Is Compounding?

Compounding is the process where an asset’s earnings, from either 澳洲幸运5官方开奖结果体彩网:capital gains or interest, are reinvested to generate additional earnings over time. This growth, calculated using exponential func🦩tions, occurs because the investment will generate earnings from both its initial principal and the accumulated earnings from preceding periods.

C🌌ompounding differs from linear growth, where only the principal earns interest each period.

Understanding Compounding

Compounding typically refers to the increasing value of an asset due to the interest earned on both the principal and the accumulated interest. This phenomenon, which is a direct realization of the 澳洲幸运5官方开奖结果体彩网:time value of money (TMV), 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 澳洲幸💖运5官ꩲ方开奖结果体彩网:dividend reinvestment plans (DRIPs) that allow investors to reinvest their cash 澳洲幸运5官方开奖结果体彩网:dividends to purchase additional shares of stock. Reinvesting in more of these dividend-paying sh💜ares 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, referred to as double compounding. In this case, not only are dividends being reinvested, but these dividend growth stocks are also increasing their per-share payouts.

Formula for Compound Interest

The formula for the 澳洲幸运5官方开奖结果体彩网:future value (FV) of a current asset relies on the concept of compound int🌼erest. 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:

$\begin{aligned}&FV = PV \times \Big (1 + \frac{ i }{ n } \Big ) ^ {nt} \\&\textbf{where:} \\&FV = \text{Future value} \\&PV = \text{Present value} \\&i = \text{Annual interest rate} \\&n = \text{Number of compounding periods per time period} \\&t = \text{The time period} \\\end{aligned}$​FV=PV×(1+ni​)ntwhere:FV=Future valuePV=Present valuei=Annual interest raten=✅Number of compounding periods per time periodt=The time period​

This formula assumes that no additional changes outside of interest are made to the origi꧒nal principal balance.

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. Twoꦇ compounding periods per year are better than one, and four compounding periods per yea♏r are better than two.

To illustrate this effect, consider the following example given the above formula. Assume that an investment of $1 million earns 20% per year. The res🧸ulting♓ future value, based on a varying number of compounding periods, is:

• Annual compounding (n = 1): FV = $1,000,000 × [1 + (20%/1)] ^{(1 x 1)} = $1,200,000
• Semiannual compounding (n = 2): FV = $1,000,000 × [1 + (20%/2)] ^{(2 x 1)} = $1,210,000
• Quarterly compounding (n = 4): FV = $1,000,000 × [1 + (20%/4)] ^{(4 x 1)} = $1,215,506
• Monthly compounding (n = 12): FV = $1,000,000 × [1 + (20%/12)] ^{(12 x 1)} = $1,219,391
• Weekly compounding (n = 52): FV = $1,000,000 × [1 + (20%/52)] ^{(52 x 1)} = $1,220,934
• Daily compounding (n = 365): FV = $1,000,000 × [1 + (20%/365)] ^{(365 x 1)} = $1,221,336

As evident, the future value increases by a smaller margin even as the number of compounding periods per year increases significantly. The frequency of compounding over a set length of time has a limited effect on an investment’s growth. This limit, based on calculus, is known as 澳洲幸运5官方开奖结果体彩网:continuous compounding and can be calculated using the formula:

$\begin{aligned}&FV=P\times e^{rt}\\&\textbf{where:}\\&e=\text{Irrational number 2.7183}\\&r=\text{Interest rate}\\&t=\text{Time}\end{aligned}$​FV=P×ertwhere:e=Irrational number 2.7183r=Interest ratet=Time​

In the above example, the future value with continuous compounding equals: FV = $1,000,000 × 2.7183 ^{(0.2 x 1)} = $1,221,404.

Compounding on Investments and Debt

Compound interest works on both assets and liabilities. While compounding boosts the value of an asset more rapidly, it can also increase the amount of money 🅠owed on a loan, as interest 😼accumulates on the unpaid principal and previous interest charges. Even if you make loan payments, compounding interest may result in the amount of money you owe increasing in future periods.

The concept of compounding is especially problematic for credit card balances. Not only is the interest rate on credit card debt high, but the interest charges also may be added to the principal balance and incur additional interest in the♔ future. For this reason, the concept of compounding is not necessarily “good” or “bad.” The effects of compounding may work for or against an investor depending on their financial situation.

Example of Compounding

To illustrate how compounding works, suppose $10,000 is held in an account that pays 5% interest annually. After the first year or compounding period, the total in the account has risen to $10,500, a simple reflection of $500 in interest being added to the $10,000 澳洲幸运5官方开奖结果体彩网:principal. In year two, the account realizes 5% growth on both the original principal and the $500 of fi𝔉rst-year interest, resulting in a second-year gain of $525 anꦓd a balance of $11,025.

After 10 years, assuming no withdrawals and a steady 5% interest rate, the account would grow to $16,288.95. Without adding or removing an💛ything from our principal balance except for interest, the impact of compounding has increased the change in balance from $500 in Period 1 to $775.66 in Period 10.

In addition, without adding new investments on our own, our investment has grown $6,288.95 in 10 years. Had the investment only paid simple interest (5% o🐻n the original investment only), annual interest would have only been $5,000 ($500 per year for 10 years).

How Will I Use This in Real Life?

If you ever buy a house, take out stu𝕴dent loans, or even apply for a credit card, you will be exposed to the effects of compounding interest. This means that not only will you pay interest on the money you borrow, but you will also owe interest on top of any interest.

But compounding interest can also work in your favor. If you put your money in a 澳洲幸运5官方开奖结果体彩网:high-yield savings account, your savings will grow much faster than they would in a checking account.

The Bottom Line

Compounding and compound interest play a very important part in shaping the financial success of investors. If you take advantage of compounding, you’ll earn more money faster. If you take on compounding d✤ebt, you’ll be stuck with a growing debt balance longer. By comp❀ounding interest, financial balances are able to exponentially grow faster than straight-line interest.