What is compound interest?
Compound interest means that the ingested interest from your principal is added back to the principal periodically, compounds on top of itself such that it generates more interest over time on the principal amount and all accumulated interest. This is a critical and potent mechanism to super-charge your capital growth, which is fundamental for a great private savings strategy. This vital, as well as the long-term development of mutual funds, equals stock market portfolios, which all owe a lot in this regard. Compounding interest, at the most fundamental level, proves why capital reinvestment is vital, as compounding should be a pillar of any investment strategy!
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
First, enter either your first deposit/investment amount or your actual balance if you already made a deposit. This figure is the basis for all calculations. Then, state the duration of your deposit or investment (generally in years), but we allow other time frames as well.
Below that is the annual interest rate; this is what you’ll see as APR on offers and comparisons of any bank product, and it does not take compounding into account. It is unrelated to the Annual Percentage Yield (APY) or Effective Annual Interest Rate, which our calculator will properly compute for you based on different compounding periods. Understand that you can not account for fees and other expenses the bank charges for processing the deposit or investment, both APR and APY.
Now, you should specify the compounding period. Your bank has it in the offers/descriptions with regard to their certificates of deposit (CDs), so if you want to ask there, The following compounding options are handled by the tool:
- annual compounding
- semiannual compounding
- quarterly compounding
- monthly compounding
- daily compounding
If on monthly, yearly, or other regular contributions, deposit it, add it on a monthly/yearly/etc., and enter how often this will contribute. Indicate whether you will pay these contributions in arrears or at the end of the period. The interest calculator will tell you with complete confidence your deposit or investment at the end of the period, any interest earned, effective interest rate, total amount deposited & the percentage of the capital increase.
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:
Other terms explained with “I” are the effective interest rate. You can modify those formulas to solve for the principal or for the time. These formulas will help you find the compound interest.
Effect of the compounding period
Interest compounding frequency, the level at which interest is added to the principal of a loan or investment, is fundamental when compared with the nominal annual interest rate, which is the effective interest rate. In this compound interest calculator, with shorter compounding periods, the effect will be visible clearly as you use the shortest possible. The most effective rate you get in compound interest (often called continuous compounding), then monthly or yearly compounding lands you at some lower percent rate.
Compound interest calculation example
In the following example, we are going to quickly figure out that certificate accrued interest, total accrued interest, and capital gain % are for a $10,000 CD with 2% annual interest over three years compounded monthly. For calculation convenience, we are not going to include any further contributions, i.e., monthly or annual.
In the first year, we use basic simple interest principles. Starting from $10,000 at a 2% interest rate, the accrued interest is $200, so at the end of the first year, it’s all summed to $10,200. Capital growth is the interest rate, in this case, very simply calculated.
In the second year, we start defer-compounding by adding $200 in interest to the principal, which means we move onto year two with $10,200. So now, the interest for this year is $10,200 * 0.02, which equates to $204. Thus, at the end of year two, the total comes out to be $10404. That gives us a growth rate of $10,404 / $10,000, which is a 4.04% increment.
The table below shows the results for years three, four, and five, along with the outcome.
| 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 APY after 5 years was $11041, with simple interest, which is just $11000. The penny-pincher tripping aside, the further compounding effect can be pretty dramatic if the rate of return is higher or the period of compounding is longer.
Simple Interest versus Compound Interest
In the above example, we have seen the distinction between simple and compound interest. To make it cuter, let’s take an example of a fictitious investment that gives a 15% annual return over a ten-year horizon. Let us now assume that the returns are reinvested at the end of every annum, earning the same rate as above. You can see the increasing difference between Simple and compound interest as the frequency of compounding increases.
$10k invested for 5 years yields >$2500. In ten years, it has goaled to over $15K. The capital growth over a period of 250%, contrasted with 405%, shows this, which demonstrates the strength of compounding. Read our post about compounding in the context of investments above.
Financial caution
Bank deposits or equivalent investments are used as a rough estimating tool for online ROI and capital growth of a bank deposit, etc. It is worth reiterating that this tool is absolutely not some silver bullet in financial planning. It is highly suggested that anyone engaging in major financial decisions and long-term commitments (i.e., very long bank deposit agreements) get professional financial advice. Users are strongly encouraged to examine the data offered by this tool and adjust their trading accordingly at their own risk.