Compound interest is interest generated on both principal and interest already accrued. Simply put, it is interest on interest.
What you need to know about compound interest:
- For investors, compound interest is your best friend because it earns interest on something other than principal.
- For borrowers, compound interest is your worst enemy because 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 the name suggests, easier to understand. It is found in amortized loans such as auto loans, student loans and mortgages, or short-term personal loans.
The difference? Compound interest includes interest earned on principal and accrued interest from any previous period. Simple interest is the interest generated only by the principal. Therefore, if both simple and compound interest have the same rate, the interest generated will always be higher during compounding.
Both types of interest are calculated at certain periods which may 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 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 the 2nd year | $ 1,100.00 | $ 1,102.50 |
Amount after the 3rd year | $ 1,150.00 | $ 1,157.63 |
Amount after 4th year | $ 1,200.00 | $ 1,215.51 |
Compound interest creates additional income of $ 15.51.
The Compound Interest Formula: A High School Mathematics Refresher Course
Advantages and disadvantages of compound interest
Depending on the type of financial instrument you manage, compound interest can help or hurt you.
Benefits of compound interest for savings and investments
Compound interest helps investors and savers to increase their initial amount faster because the growth is exponential.
Let’s say you opened an investment vehicle for a 30-year term 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 see what the amount would be after each five-year interval:
Year | Starting amount for the interval | Compound interest accrued over a five-year period | 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 |
The 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 calculated using simple interest instead, the total amount would be $ 62,500, about 72% less than with compound interest.
Interest rate in savings and investments
While the above example is a nonspecific representation of compound interest in action, the truth is, compounding can take 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 instruments such as stocks and 401 (k) reinvest earnings or interest to compose profits. The capitalization periods of these instruments and their formulas will 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 increase your debt if left unchecked. Nowhere is this more evident than with credit cards.
We can fill out 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 is only applied if the full amount of the credit card balance is not paid off in the next statement period.
For our purposes, we have $ 1,000 credit card debt with 19.99% APR.
How long would it take us to refund the credit card, assuming no further purchases were made and no fees or charges were posted, if we only paid the minimum? And what 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 | Principal paid | Interest paid | Total paid | |
Pay the minimum | $ 1,000 | $ 35 | 40 months | $ 1,031 * | $ 369 | $ 1,400 |
Pay off in one year | $ 1,000 | $ 93 | 12 months | $ 1,005 ** | $ 111 | $ 1,116 |
* The last payment of $ 35 is made when there is only $ 3.95 in debt. The excess of this payment is applied here to the principal. |
** The last payment of $ 93 is made when there is only $ 88.13 of debt remaining. 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 interest during that time.
How can this be? On the one hand, although credit card interest does not appear until the end of the billing cycle, it is compounded daily. As we have learned, the more compounding periods, the faster the amount will increase.
In this case, the $ 1,000 debt starts earning interest on the first day and continues daily until it is paid off.
If we wanted to pay it off in a year, we had to pay $ 93 per month to write off the debt. Compound interest for that year would be $ 111.
The lesson here is that if you don’t pay off all of the debt on your credit card statement by the due date, you’ll be charged compound interest on your next statement. Therefore, paying off high interest credit cards is generally recommended 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 easy as just using the formula we’ve provided above.
Different financial instruments can 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 have to do the math yourself to figure out how much you would earn in an investment account. There are many compound interest calculators online that only require you to enter the principal amount, term length, interest rate, and compounding frequency before calculating compound interest.
Compound interest faqs
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 6 and you get 12. You will double your investment in 12 years.
While the formula is too reductive to get detailed information, the Rule of 72 can help provide a quick, informal estimate of whether an investment is worth it.
What is the difference between an APR and an APY?
Both are ways of presenting interest rates as a percentage. But while APRs feature the simple interest rate, APYs include compound interest.
The APR, or Annual Percentage Rate, is the rate for making or borrowing money over the course of a year, while the APY, or Annual Percentage Yield, is the same rate but with built-in compounding periods.
The more compound periods there are, the higher the APY and the greater the difference with the APR.
Lenders typically advertise their APRs for mortgages, loans, and credit cards, while investment products and savings accounts promote their APYs.
Is Compound Interest Good or Bad?
It can be both. Investors love the payoffs that compound interest provides because it creates money effortlessly.
On the other hand, debtors despise compounding because they end up paying interest on money they haven’t even used.