Simple vs Compound Interest: What’s the Difference?

Definition of compound interest

What is compound interest?

It is different with compound interest: the interest adds to the principal, and during the next period the interest is accrued on both the principal and the interest. The interest rate stays the same (for example, 7%), but the interest amount grows faster each payment period, because you owe (or earn) the same percentage of a growing amount. This type of interest is more profitable, and therefore more appealing for investors.

Formula for compound interest and explanation of variables (P, r, n, t)

The formula of compound interest is

The variables are almost the same.

P — the principal.

r — the interest rate, represented as a decimal number.

t — the time over which the interest is calculated, usually in years.

n — how often the interest is added per year (yearly, quarterly, monthly, etc.).

A — the total amount of money (the principal and the accumulated interest).

Note that compound interest can also be calculated using:

• a spreadsheet;

• an interest calculator (available online);

• or the rule of 72: divide 72 by the interest rate to get a rough estimate of when your principal will double (in years). So, if you invest at a rate of 6%, it will take 12 years for your principal to double.

• Sometimes it is better to use another, similar rule: the rule of 70 or the rule of 73.

Remember, all these apply only to compound interest, not simple.

Example of compound interest calculation

Based on the formula, if you invest $1000 at a 5% compound interest rate and it is compounded monthly, in three years you will get $1161.47, which is more than the same principal deposited at a simple interest of 5%.

Benefits and disadvantages of compound interest

Compound interest has been investors’ favorite for decades. What are its pros and cons?

The advantages are obvious:

• your money grows exponentially;

• compounding frequency — the more often the interest adds, the better;

Compound interest is a great tool to grow your income without ongoing effort. Find more ideas in an FBS article: “29 Best Passive Income Ideas”.

However, the perks of compound interest can quickly become drawbacks, particularly when it comes to loans. The trap works the same way as with investments.

• The fast growth of the debt is especially noticeable in the case of a long-term loan, such as a mortgage. Credit cards with a short period of compounding can send debt spiraling out of control.

• The “snowball effect” of compound interest in investment still takes a lot of time: to gain a substantial profit, you should start investing early.

Weigh all the factors that affect your choice and make a balanced decision that will suit your situation and result in higher profit or minimal losses.

Comparing simple and compound interest: the main differences

Simple interest is easier to calculate and grows at a steady rate, while compound interest grows faster because it earns interest on the interest as well as the principal. Its formula is more complex.

The graph below, where P is the principal and Y is years, shows the difference in interest growth over time.

When to use each type

Understanding the distinction between simple and compound interest is essential because it has a direct impact on your savings.

In a nutshell, simple interest is more profitable in loans, while compound interest will bring you more yield in investments. Simple interest is often used for loans, especially short-term ones like car or personal loans; compound interest is widely used for mortgages or various types of long-term investments.

Compound interest can also be used in trading. To learn more, read the article on FBS: “Compound interest in trading: how to use it to increase your deposit”.

Impact of time on both types of interest

The adage "time is money" is especially true when it comes to interest rates, because time’s impact on interest rates is huge. The longer the period you invest your money for, the more yield it will earn you. In the case of simple interest, the interest earned or owed does not change. However, with compound interest, the amount grows because of the interest-on-interest snowball effect. Over long periods it is especially evident, and compound interest can make a huge difference in the total sum you will earn or owe.

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Interest accrual periods

Interest can be added to the principal at different time intervals. These intervals are called accrual periods. Some common accrual periods are:

• annually (once per year);

• quarterly (four times per year);

• monthly (12 times per year);

• daily (there are two options: 360 or 365).

Less common intervals are semimonthly, bimonthly, semiannually, and a few others.

The shorter the compounding interval, the more rapidly the interest adds. For example, daily compounding will lead to more interest earned or owed compared to annual compounding, even if the interest rate is the same.

Suppose you have invested $3000 at 7%. If it is compounded annually, in five years you will have $4207.66 in total ($1207.66 in interest), but if it is compounded daily, over the same period you will get slightly more — $4257.06 ($1257.06 in interest).

Other concepts of compound interest

• You might have come across the term continuous compounding. That’s when the interest is added continuously, over an indefinite number of periods. Continuous compounding is not used in everyday finance because it is not applicable in real life; rather, it is a mathematical idea that is important for advanced investing tasks such as forming an investment plan.

• The opposite of continuous compounding is discrete compounding. All the types of interest with set accrual periods like monthly or annually are discrete.

• Another key concept is the effective annual rate or EAR. It tells us how much you will earn or owe over a certain period of time (the real return) with the effects of compounding considered. The EAR is useful when you want to compare loans or investments with different interest conditions.
  
  Example: there are two loans with 11% interest each. One compounds annually, and the other every six months. The EAR on the latter will be higher because the more frequent the interval is, the higher the effective annual rate. This scenario, however, does not take into account the possible risks, taxes, or fees.

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Compound annual growth rate (CAGR)

When analyzing and comparing investments, factors like the compound annual growth rate, also called CAGR, can be effective. It represents the average annual growth rate of an investment or a financial metric over a certain period, provided that the profits are reinvested.

If you invest $5000 in a mutual fund, after four years your investment will grow to $7500. In this case, the CAGR of this investment is 10.67% per year.

Real-life usage examples

Simple and compound interest for different situations

Many car loans (popular nowadays) use simple interest. Suppose that you take out a loan for $30 000 at an interest rate of 7% per year for three years. The interest is calculated only on the principal amount. That means you will pay $6300 in interest over three years.

Personal loans from some banks or financial institutions also often use simple interest. For example, borrowing $5000 at a 6% annual interest rate for one year would result in $300 in interest after one year.

As for compound interest, many savings accounts use it. You put $7000 in a savings account and the interest rate is 4%, compounded monthly. So after five years you would have $8546.27 in total.

You can benefit from investments in stocks with compound interest. For example, you invest $10 000 at an annual rate of return of 7%, compounded annually, for 10 years. According to the formula, your investment will grow to $19 671.51 in 10 years.

How the choice of interest type affects the total amount

Let’s take two examples:

1. You borrow $2000 at 5% simple interest for four years. In the end, you will owe $400 in interest (see the formula), making your total repayment $2400.

2. If you borrow the same sum of $2000 at 5% compound interest compounded annually, after four years you will owe $2431.01. The interest grows a bit faster.

As you can see, compound interest leads to a larger total amount of profit or debt over time compared to simple interest.

Summary

Understanding how simple and compound interest work and how they differ is crucial for managing risk and planning your finances. Simple interest is straightforward and easy to calculate, so it is suitable for short-term loans and investments. However, compound interest can greatly increase your earnings (or debt) over time because it grows much faster. Knowing when and how each type of interest is applied can help you plan your finances and make informed decisions while saving or borrowing money. Consider the impact of time and compounding and make the most of your finances.