You may have dabbled with compounding interest equations in high school yet not had much experience with them since then.
In all likelihood, however, your finances are directly affected by compounding interest, which can be used to your advantage with savings accounts but can end up costing you big with credit card loans, student loans, and mortgages.
It is, therefore, in your best interest to have a basic understanding of what compounding is and how it works.
Compounding interest involves the process of growing, much like a snowball effect. It is the interest earned on money that was previously earned as interest.
In layman’s terms, compounding interest is “interest on interest.”
Compounding Interest Versus Simple Interest
While both compounding and simple interest will grow an investment over time, there can be huge differences in the growth achieved with the same principal amount.
Simple interest, which is easier to determine, is based on the principal amount of a loan or deposit.
To calculate the simple interest that will be earned on an investment you can use the formula I = P x R x T, where P is the “principal” amount, R is the interest rate expressed as a decimal, and T is the time the money is invested in years.
So, for example, if you invest $10,000 at a rate of 5% for three years, the calculation will be 10,000 x 0.05 x 3 = 1,500. So, the interest earned after three years is $1,500.
Compounding interest, on the other hand, is based on the principal amount of a loan or deposit as well as the interest that accumulates on it in every period.
If we were to take the above example of investing $10,000 at 5% for three years, the interest accrued would not be the same for all three years, as is the case with simple interest, since compounding interest takes into account the accumulated interest in previous periods.
How Compounding Interest Is Calculated
The rate at which compounding interest grows depends on how often the compounding occurs. The more frequent the compounding periods, the greater the compound interest earned.
This means that a higher compounding interest rate will not necessarily yield the best return.
Depending on the length of the investment, you may be better off compounding interest at a lower rate more frequently than a higher rate annually.
It is, therefore, crucial that you first do the math when considering various investment options.
The Compounding Interest Equation
There are tools available that will calculate the potential return on an investment using compounding interest, but you can also do it yourself using good old-fashioned math skills. However, unless you’re a complete math whizz, you will need a calculator with exponential functions.
The compounding interest equation is as follows:
A = P (1 + )nt
A = the total amount of money invested plus the interest accrued
P = the principal amount, i.e. the amount you put in initially
r = the interest rate expressed as a decimal
n = number of times compounding occurs per year
t = time in years
Annual Compounding Interest
When interest is compounded annually, this means that the investment grows once a year. If, for example, you invest a sum for ten years, the interest will be calculated and added ten times in total.
As a basic rule, the higher the number of compounding periods, the greater the amount of compound interest accrued.
It is possible for interest to compound quarterly, monthly, and even daily, so whenever possible, opt for interest to compound more frequently.
First, let’s have a look at how compounding interest can work to your advantage by comparing it with the previous example: $10,000 at a rate of 5% compounded annually for three years.
A = 10,000(1+ )3/1 = $11,576.25
In other words, after three years, the compounded interest will amount to $1,576.25, compared to $1,500 with simple interest.
Now, let’s have a look at how compounding interest more frequently will compare to annual compounding.
Consider the same $10,000 investment at a rate of 5% but compounded monthly for three years.
A = 10,000 (1+ )12×3 = $11,614.72
In this instance, $1,614.72 interest has been accrued simply by compounding monthly rather than annually.
Effective Compounding Interest Investments
How you can effectively invest your money will depend on several factors.
Generally speaking, time is your best ally. The earlier you begin investing, the better.
This is because your investment grows with each period of compounding interest, so the longer you can keep your money invested, the greater the interest that will accumulate.
Someone who has a good twenty years of work ahead of him will make different investment decisions compared to someone nearing retirement.
You should also consider how dependent you are on the money you’ll be investing. Can you afford to set it aside and let it grow, or will you need to access it?
The type of risk taker you are will ultimately affect how you choose to invest.
If you are a conservative investor, perhaps nearing retirement, then you may feel more comfortable dealing with less risky investments.
If you’re not averse to taking risks and are perhaps still working and accumulating a retirement nest egg, you may fare better with riskier investments.
Whatever the case, ensure you do your homework, shop around before investing, and select accounts that fit both your short- and long-term goals.
You may also consider seeking professional advice—you often need to spend a little money to make more money in the long run.
High-yield savings account
If you want a low-risk investment that grants you access to your money without incurring fees and isn’t dependent on the volatility of the market, then a high-yield savings account may suit your needs.
Online banks, in particular, can offer competitive interest rates 20 to 25 times higher than traditional savings accounts.
You’ll need to consider the initial deposit required, the minimum balance, and any fees that may be incurred, particularly if you don’t keep a specified amount in your account.
Certificates of deposit
Certificates of deposit (CDs) are offered by most banks and credit unions and can be a good option if you’re seeking a conservative investment.
CDs provide premium interest rates in exchange for an agreement to leave a lump-sum deposit untouched for a set period, usually six, twelve, or eighteen months.
You will need to keep your money tied up until the certificate of deposit matures. Otherwise, you will incur a penalty fee, so make sure you’re not investing money that acts as your emergency fund.
While CDs offer a lower opportunity for growth than higher-risk investment options, they have a guaranteed rate of return, making them a sure-fire option for making money on extra savings.
Keep an eye out for special promotions that can offer higher interest rates but may require a larger investment.
There are two types of retirement plans: the defined-benefit plan and the defined-contribution plan. While you are usually able to contribute to both, the potential payouts can differ greatly.
A defined-benefit plan is funded by the employer, but some plans allow contributions to be made by employees as well.
If you sign up for this plan, you will receive a fixed amount—usually on a monthly basis—upon retirement. The amount is determined by your salary and length of employment with the company, not on market performance.
Employees often appreciate this type of retirement plan for its stability and guaranteed income right through to their death.
A defined-contribution plan is funded by the employer whose liability to pay benefits ends once the contributions are made.
The final benefits you receive upon retirement will depend on the plan’s investment performance, meaning there is a level of risk involved.
Some plans also allow for voluntary investment by the employee, and in this case, employers often match this contribution up to a specified amount. This can prove advantageous for both the employer, who gets a tax break, and you who can use compounding interest to your advantage.
If you are able to take advantage of an employer-sponsored plan, you can contribute a portion of your current earnings into the investment plan to assist in the funding of your retirement.
In this case, any contributions made will be removed from your gross income, which means that your taxable income will be reduced.
You can then invest these extra funds into your retirement account as well, and you won’t need to pay tax on them as long as they remain in the account.
You will have to pay tax on these earnings once you begin withdrawing from your retirement fund, but by deferring tax on contributions made, you will be able to reinvest your income, the interest made, and capital gains, which will yield a much higher rate of return before retirement thanks to the snowballing effect of compounding interest.
Upon retirement, you’ll have two choices for the distribution of your fund. You can either receive periodic payments, usually monthly, for the remainder of your life or a lump-sum payment.
Some plans will allow a combination of the two so that you can receive a partial payment but allow the rest of your funds to continue earning interest for you.
Bonds can be a good option for risk-averse investors looking for alternatives to buying stocks.
When you buy a bond, you loan a sum to the issuer for a predetermined period. In exchange, the issuer agrees to regular interest payments, usually every six months, until the bond reaches maturity and then repays the principal amount.
Corporate bonds, issued by corporations, tend to offer higher interest rates, but they are taxable at both the state and federal level.
Municipal bonds are issued by states and cities to fund public projects and services.
While the interest paid is lower than on corporate bonds, it is exempt from federal taxes. And if you buy bonds issued by your home state, then municipal bonds are exempt from state and local taxes as well.
Treasury bonds (T-bonds) are issued and backed by the U.S. government, making them a practically risk-free investment. While the interest paid, which is lower than corporate bonds, is exempt from state and local taxes, it is taxable at the federal level.
Keep in mind that you can only buy bonds through a dealer, and he will require a commission. These commissions, or mark-ups, are bundled into the price of bonds, and it is not always clear how much you are being charged.
Mark-ups will reduce a bond’s yield, and consequently, your total returns. Make sure you do your research first and ask for transparency from potential dealers.
If you're not averse to a little risk-taking, then investing in stocks could be for you. And if you play your stocks right, then the potential rewards are higher than other investment options.
Contrary to popular belief, the money to be made in the stock market is not through frequent buying and selling but through “buying and holding,” a strategy popularized by Benjamin Graham, the father of value investing.
If you decide to invest in stocks, you should focus on the total return and commit to investing for the long term.
You can increase your chances of profitability by selecting stock from well-run companies with sound finances and a reputation for good management practices. You should also plan to hold your stocks for a minimum of five years.
Through careful planning and research, finding suitable investment options that will meet your short- and long-term goals is feasible.
Ensure you take into account the potential risks and rewards of each option, and then, hopefully, you can sit back and let your money and compounding interest work for you.