Compound interest is the interest earned on both principal and interest already accrued. Simply put, it’s interest on interest.
What you need to know about compound interest:
- For investors, compound interest is your best friend because it generates interest on something other than the principal.
- For borrowers, compound interest is your worst enemy as it increases debt as it is calculated not only from the principal still owed but also from the unpaid interest previously generated.
- Calculating compound interest is complicated. The way to calculate it depends on the type of financial instrument, the type of rate used (APR or APY), the number of compounding periods and other factors.
The difference between simple interest and compound interest
Compound interest can be found in savings accounts, certificates of deposit, investment vehicles, loans, and credit cards.
Simple interest is, as its name suggests, easier to understand. It can be found in amortized loans such as car loans, student loans and mortgages, or short-term personal loans.
The difference? Compound interest includes interest earned on principal and accrued interest from any prior period. Simple interest is the interest generated only by the principal. Therefore, if simple and compound interest have the same rate, the interest generated will always be higher when compounding.
Both types of interest are calculated at certain periods which can be annual, semi-annual, quarterly, monthly, daily or any other period defined by the financial institution.
Let’s compare two scenarios with an initial principal of $1,000, both with an interest rate of 5% calculated annually, but one has simple interest while the other has compound interest.
Calculation period | With a simple interest | With compound interest |
Initial amount | $1,000.00 | $1,000.00 |
Amount after the 1st year | $1,050.00 | $1,050.00 |
Amount after 2nd year | $1,100.00 | $1,102.50 |
Amount after the 3rd year | $1,150.00 | $1,157.63 |
Amount after the 4th year | $1,200.00 | $1,215.51 |
Compound interest creates additional income of $15.51.
The Compound Interest Formula: A High School Math Refresher Course
Advantages and disadvantages of compound interest
Depending on the type of financial instrument you manage, compound interest can help or hurt you.
How Compound Interest Benefits Savings and Investments
Compound interest helps investors and savers grow their initial amount faster because the growth is exponential.
Let’s say you opened an investment vehicle for a term of 30 years with a compound rate of return of 5%. Interest is calculated at the end of each year, giving the instrument 30 compounding periods. Let’s look at what the amount would be after each five-year interval:
Year | Starting amount for the interval | Compound interest accrued over a period of five years | Total with compound interest at the end of the interval |
5 | $25,000.00 | $6,907.04 | $31,907.04 |
ten | $31,907.04 | $8,815.33 | $40,722.37 |
15 | $40,722.37 | $11,250.83 | $51,973.20 |
20 | $51,973.20 | $14,359.24 | $66,332.44 |
25 | $66,332.44 | $18,326.43 | $84,658.87 |
30 | $84,658.87 | $23,389.69 | $108,048.56 |
Total accrued interest for all 30 years is $83,048.56. The magic of compound interest turned $25,000 into $108,048.56.
If the return were instead calculated with simple interest, the total amount would be $62,500, or about 72% less than with compound interest.
Interest rates on savings and investments
Although the example above is a non-specific representation of compound interest in action, the truth is that compounding can take many different forms and be calculated in different ways.
Financial instruments such as certificates of deposit (CDs) or high yield savings accounts also have compound interest. However, while CDs generally have fixed interest rates, savings accounts tend to have variable rates that can change daily due to market fluctuations.
Investment vehicles such as stocks and 401(k)s reinvest earnings or interest in compound earnings. The capitalization periods of these instruments and their formulas vary but the principle is the same: exponential growth for the benefit of the investor.
How Compound Interest Affects Your Debt
In the same way that compound interest can help you grow your income faster, it can also inflate your debt if left unchecked. Nowhere is this more evident than with credit cards.
We can fill a book trying to explain how credit card interest is calculated. But let’s try to simplify the process and focus on how compound interest works in this case. Remember that credit card interest only applies if the full amount of the credit card balance is not paid off during the next statement period.
For our purposes, we have credit card debt of $1,000 with an APR of 19.99%.
How long would it take to pay off the credit card, assuming no more purchases made and no fees or charges were posted, if we only paid the minimum? And how much interest would be generated? What would our monthly payment be if we decided to pay off the debt in one year?
Credit card balance | Monthly payment | Payment time | Capital paid | Interest paid | Total paid | |
Pay the minimum | $1,000 | $35 | 40 months | $1,031* | $369 | $1,400 |
Payback in one year | $1,000 | $93 | 12 months | $1,005** | $111 | $1,116 |
*The last payment of $35 is made when only $3.95 remains in debt. The excess of this payment is applied here to the principal. |
**The last payment of $93 is made when only $88.13 remains in debt. The excess of this payment is applied here to the principal. |
With a minimum payment, it would take us 40 months to pay off the credit card with $369 in interest payments during that time.
How can this be? For one, although credit card interest doesn’t accrue until the end of the billing cycle, it’s compounded daily. As we learned, the more compounding periods, the faster the amount will grow.
In this case, the $1,000 debt starts earning interest on day one and continues daily until it is paid off.
If we wanted to pay it off in a year, we would need to pay $93 a month to clear the debt. Compound interest for that year would be $111.
The lesson here is that if you don’t pay all of your credit card statement debt by the due date, you’ll be charged compound interest on your next statement. Therefore, it is generally recommended to pay off high interest credit cards to avoid inflating debt.
Use a compound interest calculator
Although you already know how compound interest works, you might want to learn how to calculate it. You can even try using an Excel formula. But calculating compound interest is complicated, and it’s usually not as simple as just using the formula we provided above.
Different financial instruments may calculate it in different ways, and other times you will need to perform additional calculations to determine interest rates, such as with credit card APRs.
However, you don’t need to do the math yourself to determine how much you would earn in an investment account. There are many online compound interest calculators that only require you to enter the principal amount, term length, interest rate, and compounding frequency before calculating compound interest.
Compound Interest FAQ
What is the rule of 72?
A quick and easy way to determine how long it will take for an investment to double, given a fixed interest rate. All you have to do is divide 72 by the interest rate and you get the number of years.
For example, if you have an interest rate of 6%, divide 72 by six and you get 12. You will double your investment in 12 years.
Although the formula is too reductive to obtain detailed information, the rule of 72 can help provide a quick and informal estimate to determine if an investment is worth it.
What is the difference between APR and APY?
Both are ways of presenting interest rates as a percentage. But while APRs show the simple rate of interest, APYs include compound interest.
APR, or Annual Percentage Rate, is the rate for earning or borrowing money over the course of a year, while APY, or Annual Percentage Return, is the same rate but with compounding periods integrated.
The more compounding periods, the higher the APY and the greater the difference with the APR.
Lenders will typically advertise their APRs for mortgages, loans, and credit cards, while investment products and savings accounts will advertise their APYs.
Is compound interest good or bad?
It can be both. Investors love the gains that compound interest provides because it creates money effortlessly.
On the other hand, debtors despise capitalization because they end up paying interest on money they haven’t even used.