Calculating Compounding Interest
Use our compound interest calculator to estimate how your savings will grow over time through compound interest. Enter your initial investment amount, rate of return, compounding frequency, and years of growth to see how your savings increases over time.
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How to Use our Compound Interest Calculator
You only need to enter four simple numbers in our compound interest calculator to find how an investment would grow over time using compound interest.
1. Your initial deposit:
Enter your initial investment amount.
2. Years to save
The number of years you intend to keep your money invested.
3. Rate of return
4. Compounding Frequency
Select either daily compounding, monthly compounding, or annual.
NOTE: Compounding frequency is how often the bank or insurance company credits interest to your account.
Compounded daily means that if you earn interest one day that interest starts earning interest the very next day. Monthly or annual compounding interest takes a little longer for the interest you’ve earned to start earning additional interest.
Click the Calculate Button
Your results display immediately below the calculator. The amount is how much money you will have at the end of the period you selected.
What is Compound Interest?
Compound interest is the financial term used to describe the process of earning interest on interest and can help your savings grow more quickly over time. The power of compound interest is greater the longer you keep your money invested.
The way interest is credited to investment has a significant impact on how your investment grows. Compound interest is often calculated on retirement savings, certificates of deposits (CD), and fixed annuities.
On the other hand, simple interest only credits interest on your initial investment. If you earned 6% simple interest on a $100,000 investment you would earn $6,000 each year. You would have $106,000 at the end of the first year, $112,000 at end of two years, and $118,000 at the end of year three.
If a $100K earned 6% compounded annually you would have $106,167.78 after one year, $112,715.98 after two years, and $119,668.05 after three years.
Compounding Interest Annually Example
The graph above shows how a $10,000 savings account earning 15% interest compounded annually would grow over a 40-year period of time. You can see in the table below the $10,000 grew to $123,755 after 20 years and to $2,329,248 at the end of 40 years.
|Year||Principal||Annual 15% interest||Principal after interest|
Compound Interest Formula
A compound interest calculator makes calculating compound interest an easy task but you can also calculate compounding interest in Excel or by hand using a simple compound interest formula.
This calculator uses the compound interest formula to find principal plus interest.
A = P(1 + r/n)nt
In the formula
A = Accrued amount (principal + interest)
P = Principal amount
r = Annual nominal interest rate as a decimal
R = Annual nominal interest rate as a percent
r = R/100
n = number of compounding periods per unit of time
t = time in decimal years; e.g., 6 months is calculated as 0.5
APY vs. Interest Rate
APY is the annual interest rate, taking compounding into account. Annual percentage yield or effective annual yield is the analogous concept for savings or investments, such as a certificate of deposit. Since a loan by a borrower is an investment for the lender, both terms can apply to the same transaction, depending on the point of view.
ANNUAL PERCENTAGE YIELD. — The term “annual percentage yield” means the total amount of interest that would be received on a $100 deposit, based on the annual rate of simple interest and the frequency of compounding for a 365-day period, expressed as a percentage calculated by a method which shall be prescribed by the Board in regulations.
For financial institutions in the United States, the calculation of the APY and the related annual percentage yield earned are regulated by the FDIC Truth in Savings Act of 1991.
Frequently Asked Questions
Rule of 72
The Rule of 72 determines the time for an investment to double in size, depending on its rate of return. Divide 72 by the rate of return to calculate the doubling period.
For example, if an investment pays an 8% annual compounded rate, it will double in value in approximately nine years (72 / 8 = 9).
The formula for the compound interest is derived from the difference between the final amount and the principal, which is: CI = Amount – Principal. The formula of monthly compound interest is:
CI = P(1 + (r/12) )12t – P
- P is the principal amount,
- r is the interest rate in decimal form,
- t is the time.
Continuous compound interest
Continuously compounding interest represents the mathematical limit that compound interest can reach within a specified period. The continuous compound equation is represented by the equation below:
At = A0ert
At : amount after time t
r : interest rate
t : number of years
e : mathematical constant e, ~2.718
For instance, we wanted to find the maximum amount of interest that we could earn on a $1,000 savings account in two years.
Using the equation above:
At = $1,000e(6% × 2)
At = $1,000e0.12
At = $1,127.50
As shown by the examples, the shorter the compounding frequency, the higher the interest earned. However, above a specific compounding frequency, depositors only make marginal gains, particularly on smaller amounts of principal.