Simple Interest vs. Compound Interest: The Main Differences

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Simple Interest vs. Compound Interest: An Overview

Interest is the amount of money that you must pay to borrow money in addition to the principal of the loan. It’s also the amount that you are paid over time when you deposit money in a savings account or certificate of deposit. You are essentially loaning money to the bank and it is paying you interest.

The interest rate is a percentage of the amount of the loan, such as 4%.

But the percentage paid can be radically different in real dollar terms depending on whether it is calculated as simple interest or compound interest:

• Simple interest is the percentage of a loan amount that will be paid by the borrower annually in addition to paying the loan principal.
• Compound interest may be the same percentage rate but it is calculated periodically. Every time it is calculated, the new interest payment is added to the principal amount, thus increasing the dollar amount due every time it is calculated. In other words, your interest is earning interest.

Key Takeaways

• Interest is the cost of borrowing money, expressed as a percentage of the total amount of the loan.
• Simple interest is an annual percentage of the amount borrowed, referred to as the annual interest rate.
• Compound interest is based on the sum of the principal amount and the previous interest payments on it.
• So, if interest on an account is compounded daily, the interest paid is higher by a fractional amount every day.

Simple Interest

Simple interest is the annual percentage of a loan amount that must be paid to the lender in addition to the principal amount of the loan. The total dollar amount of interest is determined by the length of time it takes for the loan to be repaid.

Simple interest is calculated using the following formula:

$begin{aligned} &text{Simple Interest} = P times r times n \ &textbf{where:} \ &P = text{Principal amount} \ &r = text{Annual interest rate} \ &n = text{Term of loan, in years} \ end{aligned}$​Simple Interest=P×r×nwhere:P=Principal amountr=Annual interest raten=Term of loan, in years​

To find simple interest, multiply the original borrowed (principal amount) by the interest rate (annual interest rate), written as a decimal instead of a percentage. To change a percentage into a decimal, divide the amount by 100 or move the decimal point in the percentage figure two places to the left—for example, 5% can be changed to .05.

Then, multiply that number by how long you’ll leave the money in the account or the loan time (term of the loan in years).

Simple Interest Example

Let’s say a student gets a loan to pay for one year of college tuition. The original amount is $18,000. The loan’s annual interest rate is 6%. The student gets a great job after graduation, cuts spending, and repays the loan over three years. How much interest will the student pay in total?

To find the answer, multiply the original amount borrowed ($18,000) by the interest rate (6% becomes .06). This amount is $1,080. The student will pay $1,080 per year in interest.

Then multiply that number by the loan term, or years of repayment, which is three years. This amount is $3,240. The student will repay $3,240 over that time.

So the quick formula to find the simple interest the student will pay is:

$begin{aligned} &$3,240 = $18,000 times 0.06 times 3 \ end{aligned}$​$3,240=$18,000×0.06×3​

How much will the student pay back in total, including the principal and all interest payments? Add the principal amount ($18,000) plus simple interest ($3,240) to find this. The student will repay $21,240 in total to borrow money for college.

$begin{aligned} &$21,240 = $18,000 + $3,240 \ end{aligned}$​$21,240=$18,000+$3,240​

Compound Interest

Compound interest is more complicated. Unlike simple interest, compound interest accrues or builds over time. You earn interest on the principal plus any interest that was paid previously.

If you’re borrowing money with compound interest, this means you’ll pay interest on the principal plus any interest that has built up. If you’re depositing money in the bank, it means the interest payment on your money will grow over time in real dollar terms.

Interest may be compounded daily, monthly, quarterly, semiannually, or annually. The more often it’s compounded, the more you earn or pay.

The formula for compound interest is:

$begin{aligned} &text{Compound Interest} = P times left ( 1 + r right )^t – P \ &textbf{where:} \ &P = text{Principal amount} \ &r = text{Annual interest rate} \ &t = text{Number of years interest is applied} \ end{aligned}$​Compound Interest=P×(1+r)t−Pwhere:P=Principal amountr=Annual interest ratet=Number of years interest is applied​

Compound Interest Example

Imagine you have an interest rate of 10%, a principal amount of $100, and a period of two years.

Use the formula to calculate the total amount you’ll pay back or earn in interest:

• P = $100
• r = 10% or 0.10
• t = 2
• $100 x (1 + 0.10)2 – $100
• $100 x (1.10)2 -$100
• $100 x 1.21 – $100
• $121 – $100 = $21

It might be easier to use an online calculator, but it’s good to understand how the formula works.

More Simple Interest vs. Compound Interest Examples

Below are some examples of simple and compound interest.

Example 1: Simple Interest

Suppose you put $5,000 into a 1-year certificate of deposit (CD). The CD pays simple interest at 3% per year. The interest you earn after one year is $150:

$begin{aligned} &$5,000 times 3$​$5,000×3%×1​

Example 2: Simple Interest

Suppose you don’t want to get a 1-year CD but a 4-month CD.

If you cash the CD after 4 months, how much would you earn in interest if the interest rates are based on an annual rate?

You would receive $50. You multiply the principal ($5,000) by the annual interest rate (3% or 0.03) by the months the CD was active (4 out of 12 months).

$begin{aligned} &$5,000 times 3$​$5,000×3%×124​​

Example 3: Simple Interest

Suppose after college you want to start a business creating a cool new app. To fund all the costs involved, you borrow $500,000 for 3 years from a wealthy aunt, paying 5% simple interest. You plan to repay the loan in 3 years in one lump sum, with profits you make after someone buys your business.

How much would you have to pay in interest charges every year in the meantime? You have to pay $25,000 in interest charges every year, using the below formula:

$begin{aligned} &$500,000 times 5$​$500,000×5%×1​

What would your total interest charges be after 3 years? You would pay $75,000 in total interest charges after 3 years, using the below formula:

$begin{aligned} &$25,000 times 3 \ end{aligned}$​$25,000×3​

Example 4: Compound Interest

Continuing with the above example, suppose you still believe in the company and need to borrow an additional $500,000 for 3 more years. Unfortunately, your rich aunt is tapped out but has granted you an extension on repaying her.

So, you apply to a bank for a loan at an interest rate of 5% per year. But this time, the interest is compounded annually. The entire loan amount and interest are payable after three years. What would be the total interest you pay?

Since compound interest is calculated on the principal and accumulated interest, here’s how it adds up:

$begin{aligned} &text{After Year One, Interest Payable} = $25,000 text{,} \ &text{or } $500,000 text{ (Loan Principal)} times 5$​After Year One, Interest Payable=$25,000,or $500,000 (Loan Principal)×5%×1After Year Two, Interest Payable=$26,250,or $525,000 (Loan Principal + Year One Interest)×5%×1After Year Three, Interest Payable=$27,562.50,or $551,250 Loan Principal + Interest for Years Oneand Two)×5%×1Total Interest Payable After Three Years=$78,812.50,or $25,000+$26,250+$27,562.50​

You can also calculate your total interest using the compound interest formula from above:

$begin{aligned} &text{Total Interest Payable After Three Years} = $78,812.50 text{,} \ &text{or } $500,000 text{ (Loan Principal)} times (1 + 0.05)^3 – $500,000 \ end{aligned}$​Total Interest Payable After Three Years=$78,812.50,or $500,000 (Loan Principal)×(1+0.05)3−$500,000​

This shows how compound interest quickly adds up when borrowing—and how carefully you should consider big loans that you pay back over a long time.

Which Is Better, Simple or Compound Interest?

It depends on whether you’re saving or borrowing. Compound interest is better for you if you’re saving money in a bank account or being repaid for a loan.

If you’re borrowing money, you’ll pay less over time with simple interest.

Simple interest really is simple to calculate. If you want to know how much simple interest you’ll pay on a loan over a given time frame, simply sum those payments to arrive at your cumulative interest.

How Do Teens Benefit From Compound Interest?

Teens have the advantage of youth and time. The earlier you start saving money, the more money you earn in interest. If it is compound interest, your interest earns interest, meaning you’re earning more every time interest is paid. Keep adding to your savings to increase your earnings even more.

What is the Rule of 72?

The Rule of 72 helps you estimate how long it will take your investment to double if you have a fixed annual interest rate. Divide the number 72 by your investment’s interest rate. For example, if your interest rate is 4%, divide 72 by 4. You get 18. It will take roughly 18 years for your investment to double in value.

The Rule of 72 is more accurate for lower rates of return.

The Bottom Line

Compound interest can benefit you greatly, particularly if you’re young with many years to save ahead of you. Compound interest earns you more money in your bank account, even if you don’t add to your account in the meantime.

But if you borrow money, you’ll pay more with compound interest, and the shorter the compounding period, the more you’ll pay over time.

Understanding these formulas can help you see why it makes good sense to save early and leave the money in the account for as long as possible—and why it’s usually best to pay off loans quickly if you can.

Read the original article on Investopedia.