Compound Interest Calculator
This compound interest calculator computes the interest, future value, and other values related to a deposit and/or periodic contributions after a given period of time. It also gives out the accumulation of the balance over the time. To use the calculator, please fill in the appropriate fields such as interest rate, hold time, and compounding frequency, then click the "Calculate" button.
What is Compound Interest?
In finance, interest is the price that money earns for being borrowed, saved, or invested. If you borrow money, then interest is the price you pay the lender. If you open a savings account, then interest is the price you earn for storing money at the bank.
Compound interest, then, is the interest earned (or charged) on interest.
Compound interest is calculated by adding accrued interest to an original balance, like a loan or savings deposit. Then, the next interest payment is calculated based on the original amount plus the added interest.
For example, say you put $100 in a savings account that compounds annually at 10% interest. Your first year, you'll earn $10 on your deposit. But in your second, you'll earn $11, because now you're earning interest on your deposit plus your interest of the first year, which is $100 + $10 = $110.
Because compounding earns interest exponentially, it's handy for building savings quickly – but detrimental when you're repaying a debt.
Where to Find Compound Interest
Compound interest can work either for or against you, depending on where it shows up. Nearly all the borrowing and lending in modem society use compound interest.
As a saver and investor, you can find compound interest in places like:
- Savings and money market accounts
- Brokerage accounts
- Retirement accounts (like your 401(k) or IRA)
As a debtor, compound interest most commonly shows up on credit cards and some personal loans. Most student loans, mortgages, and auto loans also use compound interest.
Compound Interest vs. Simple Interest
Compound interest is not the same as its cousin, simple interest.
Compound interest is calculated on the principal (loan or deposit amount) plus accumulated interest.
By contrast, simple interest is calculated only on the original loan or deposit amount.
For instance, say you deposit $100 into a savings account that earns simple interest of 10% annually. Since your account only earns interest on your original balance, your annual earnings would stay steady at $10.
By comparison, in a compound interest scenario, your annual earnings would increase as your interest adds to your balance.
How Does Compound Interest Work?
Compound interest works by making the balance of a deposit or loan grow exponentially. But how quickly the balance grows depends on both the interest rate and compounding frequency.
Compounding describes how often earned interest adds to the principal. The more frequently a balance compounds, the faster it grows.
Common compounding schedules include daily, monthly, quarterly, or annually. Some balances also compound continuously.
If you're the one earning interest, more frequent compounding is preferable, as your funds grow faster. But if you're paying interest, you want your balance to compound as infrequently as possible.
How to Calculate Compound Interest
The basic compounding formula looks like this:
| A = P (1 + |
|
) | nt |
In this equation:
- A = the final amount
- P = your principal (the starting balance, such as an initial deposit or loan amount)
- r = the annualized interest rate expressed as a decimal (for instance, 10% = 0.10)
- n = the number of times interest compounds in a year
- t = time period in years
Using this calculation gets you A, or the final amount equal to the interest earned plus the initial balance. If you want to find just the interest earned, simply follow the formula, then subtract your starting balance (P) from your final value (A).
An Example of Compound Interest
Let's give a quick example of how to use the above formula.
Say you put $10,000 into a savings account that pays 10% interest, compounded monthly, for 6 months. In this example:
- P = $10,000
- r = 10%, or 0.10
- n = 12
- t = 0.5
Now, we simply plug these numbers into our formula to get the answer:
| A = | $10,000(1+ |
|
)(12)(0.5) | |||
| = | $10,000(1.0083333333)6 | |||||
| = | $10,510.53 | |||||
In other words, in six months, your $10,000 will grow by $510.53.
But that's a lot of work to reach a number that you'll have to double-check for accuracy. Instead of fiddling with a pencil and calculator, you can rely on our calculator instead. Not only is it faster, but you can easily add extra variables, too!
The Compound Interest Calculator
Our calculator makes it easy to compute the interest, future value, total contributions, and more on a deposit. Each calculation also produces a handy pair of graphs to illustrate how your earnings grow over time. Plus, we provide an easy-to-understand breakdown of your initial deposit, contributions, and interest.
Before you start your calculation, it's important to gather some basic numbers to enter into the following fields of the calculator:
- Initial deposit: This is your starting sum, such as a savings account deposit.
- Contribute: This is where you add any additional contributions that increase your deposit. You can choose to add your sum at the beginning or end of each period, ranging from yearly to daily.
- Holding time: This is where you enter, in months and years, how long you plan to let your deposit earn interest.
- Interest rate: This is the annualized interest rate you earn on the deposit in question.
- Compound: This is how often your account compounds, set in intervals from daily to annually, continuously, or self-defined. (The faster a balance compounds, the faster it grows.)
Once you have these values, using the Compound Interest Calculator is easy. Just fill in the relevant fields and click "Calculate." That's it!
Example of a Compound Interest Calculation
Let's give a quick example of how our calculator works.
Say that you put down an initial deposit of $10,000 in a high-yield savings account that earns 7% interest compounded monthly. You decide to keep the account for 10 years and make a $100 deposit at the beginning of each month.
Your $10,000 deposit and $12,000 total of monthly contributions earns cumulative interest of $15,506.06, resulting in a future value of $37,506.06. The APY is 7.229%.
It's that easy!
What is APY?
As you see in the calculation above, when you enter a 7% interest rate in the calculator, the results spit out a 7.229% APY. So, what's with the different numbers?
APY stands for annual percentage yield. Your APY takes into account the impacts of compounding interest on a given calculation. In other words, it reflects your real rate of return (ROR) on annual base. Since your account balance grows with each compounding period, the interest you earn on your balance grows, too.
Note that your APY is similar to the annual percentage rate (APR) that lenders report for their loans. While they both standardize your interest rate, there are two significant differences:
- APR considers fees, but not the effects of compounding
- APY considers the effects of compounding, but not fees
How to Take Advantage of Compound Interest
Now that you know what compound interest is and how to calculate it, you can make it work for you. A few tips include:
- Saving early and often. The longer your money has to grow, and the more of it there is, the faster you'll accumulate wealth.
- Reinvest when possible. As an investor, you can maximize your compound interest by reinvesting your stock or bond dividends. Using investment income to buy more investments means you have more assets to generate wealth.
- Compound as frequently as possible. If you have the option between two identical accounts with different compounding frequencies, compound more often. More frequent compounding results in greater growth.
- Pay off compounding and high-interest debts first. When you borrow money, compound interest works against you. Tackling compounding and high-interest debts most aggressively can save you buckets of cash long-term.