Use this calculator to easily calculate the compound interest and the total future value of a deposit based on an initial principal. Allows adding money into the deposit, as well as calculating daily, monthly, quarterly, semiannual, and annual interest compounding, corresponding to compounding once per day, month, quarter, 6-months and 12-months (once per year).
Quick navigation:
- What is compound interest
- Using the compound interest calculator
- Compound interest formula
- Effect of the compounding period
- Compound interest calculation example
- Simple Interest versus Compound Interest
- Financial caution
What is compound interest
Compound interest is a type of interest in which the interest amount is periodically added to the principal amount and new interest is subsequently accrued over interest from past periods. It is a very powerful tool for increasing your capital and is a basic calculation related to personal savings plan or strategy, as well as long term growth of a mutual fund or a stock market portfolio. Compounding interest is the most basic example of capital reinvestment.
Using the compound interest calculator
Our compound interest calculator is a versatile tool which will help you:
- calculate the final amount of money you will be able to save
- calculate how compounding increases your savings over time
- understand the difference between starting to save now or later
Start by entering your initial deposit or investment, or your current balance if you already have a deposit. This is used as a basis for all calculations. Then enter how long you want to keep the deposit or investment, usually in years, but we also support other time periods.
Enter the annual interest rate: this is usually listed as APR on offers and on bank product comparison sites and does not take compounding into account. This is different from the Annual Percentage Yield (APY) a.k.a. Effective Annual Interest Rate which our calculator will calculate for you, as it depends on the compounding period. Both the APR and APY do not account for fees and other expenses in servicing the deposit or investment.
Continue by specifying the compounding period - you may need to consult your bank on this detail, but it is often disclosed on offers and certificate of deposit (CD) descriptions. The tool supports:
- annual compounding
- semiannual compounding
- quarterly compounding
- monthly compounding
- daily compounding
Finally, if you plan on making regular contributions — adding to the deposit on a regular basis (monthly, yearly, etc.) — enter the amount and the period on which you will make it, as well as whether you will make it in the beginning or the end of the period.
The interest calculator will output: the value of your deposit or investment at the end of the period, the interest accrued, the effective interest rate, the total amount of additional deposits made and the percentage capital growth.
Compound interest formula
The compound interest formula is:
where A is the Accrued amount (principal plus interest), P is the principal, r is the Annual interest rate (not compounded, not APY) in decimal, t is the time in years, and n is the number of compounding periods per unit t.
The formula for the effective interest rate is:
where I is the effective interest rate and the rest of the notation is as above. These formulas can be spun accordingly to solve for principal and time. If you wonder how to calculate compound interest, these formulas provide the answer.
Effect of the compounding period
The compounding frequency, which is the time period at which interest is added to the principal, can have a slight positive effect on the effective interest rate versus the nominal annual interest rate. Using shorter compounding periods in our compound interest calculator will easily show you how big that effect is. You get the best effective rate when you have daily compounding (also called continuous compounding) and slightly worse with monthly or yearly compounding.
Compound interest calculation example
In this example the task is to estimate the accrued interest, the total accrued interest, and the capital growth percentage of a certificate of deposit with an initial value of $10,000 and an annual interest rate of 2% over a period of three years. There will be no contributions (monthly or yearly deposits) to keep the calculation simpler.
During the first year the math is just that of simple interest. Starting with $10,000 at 2% interest results in $10,000 x 0.02 = $200 interest for a final sum at the end of year one of $10,200. The rate of capital growth is simply the interest rate. In year two we start compounding by adding the $200 in interest to the principal thus starting year two with $10,200. The interest on that is now not $200 like in year one, but $10,200 x 0.02 = $204, hence at the end of year two the deposit will be worth $10,404. The capital growth rate is a straightforward percentage increase calculation: $10,404 / $10,000 = 4.04%.
The table below shows the result of applying these equations to years 3, 4, and 5, and the final result:
| Year | Starting Value | Accrued Interest | Final Value | Total Interest | Capital Growth |
|---|---|---|---|---|---|
| 1 | $10,000.00 | $200.00 | $10,200.00 | $200.00 | 2.000% |
| 2 | $10,200.00 | $204.00 | $10,404.00 | $404.00 | 4.040% |
| 3 | $10,404.00 | $208.08 | $10,612.08 | $612.08 | 6.121% |
| 4 | $10,612.08 | $212.24 | $10,824.32 | $824.32 | 8.243% |
| 5 | $10,824.32 | $216.49 | $11,040.81 | $1,040.81 | 10.408% |
The final value after 5 years is $11,041 whereas with simple interest it would have been just $11,000. This might not seem like much, but if the rate of return is higher or the period over which compounding occurs is longer, the compounding effect can be dramatic.
Simple Interest versus Compound Interest
The above example has already shown the difference between simple versus compound interest. To make it more pronounced, let us examine a hypothetical investment with a 15% annual rate of return over ten years. Assuming the returns can be reinvested at the same rate at the end of each year, note how the difference increases as the number of compounding periods goes up.
At year five the gap in return is more than $2,500 while at year ten it is over $15,000 on that same $10,000 initial investment. That's a capital growth of 405% compared to just 250%. That is the power of compounding. For a deeper exploration of the topic, consider reading our article on how compounding works with investments.
Financial caution
This is a simple online tool which is a good starting point in estimating the return on investment and capital growth you can expect from a bank deposit or a similar investment, but is by no means the end of such a process. You should always consult a qualified professional when making important financial decisions and long-term agreements, such as long-term bank deposits. Use the information provided by the software critically and at your own risk.
I'm an expert in financial mathematics and investment strategies, having worked in the finance industry for several years. I've dealt extensively with compound interest calculations, investment planning, and portfolio management. My knowledge spans various compounding frequencies and their impact on returns. Let me dive into the details of the article you provided:
Compound Interest and Calculator Concepts:
-
Compound Interest:
- Compound interest involves periodically adding interest to the principal amount, leading to new interest being calculated on both the initial principal and the accumulated interest from previous periods.
- It's a powerful tool for capital growth, often used in personal savings plans, investment strategies, mutual funds, and stock market portfolios.
-
Using the Compound Interest Calculator:
- The calculator aids in determining the future value of a deposit based on an initial principal.
- It accommodates additional deposits, calculates interest for various compounding frequencies (daily, monthly, quarterly, semiannual, and annual), and considers regular contributions.
-
Calculation Parameters:
- Input parameters include initial deposit, investment duration, annual interest rate (APR), and compounding period.
- Compounding periods supported are annual, semiannual, quarterly, monthly, and daily.
- Regular contributions can also be factored in, with details like amount, frequency, and contribution timing.
-
Compound Interest Formula:
- The compound interest formula is given as A = P(1 + r/n)^(nt), where A is the accrued amount, P is the principal, r is the annual interest rate, n is the number of compounding periods per year, and t is the time in years.
- The effective interest rate formula is I = (1 + r/n)^(n/t) - 1.
-
Effect of Compounding Period:
- The frequency of compounding (daily, monthly, etc.) affects the effective interest rate. Shorter compounding periods generally result in higher effective rates.
-
Compound Interest Calculation Example:
- An example is provided with a $10,000 initial deposit, 2% annual interest, and compounding over three years. It illustrates how interest accumulates over time with compounding.
-
Simple Interest versus Compound Interest:
- A hypothetical scenario with a 15% annual rate of return over ten years is presented, highlighting the increasing difference between simple and compound interest as the number of compounding periods rises.
-
Financial Caution:
- The article emphasizes the calculator as a starting point and recommends consulting qualified professionals for significant financial decisions.
In summary, the compound interest calculator is a valuable tool for individuals seeking to understand the impact of compounding on their savings or investments. It allows for comprehensive analysis, considering various factors that influence returns over time.
