Simple Compound Calculator
What Is Compounding Interest
Interest is the price of a loan or the increase in the value of an investment. Either way, it is a proportional value (usually expressed in percentage), which is added to the monthly payment or the principal (money deposited into an investment or the money borrowed when regarding a loan).
Interest can be calculated in several ways, but most commonly there is simple interest or basic compound interest.
The main difference between them lies in what part of the principal is the interest calculated out of.
In the case of the simple interest, it is calculated once from the initial sum. This sum is then added during each period to the principal. In other words, the simple interest is an absolute number value and the same value is being added over time.
Compound interest is a little more complicated, as each new added value is different (increasing in the case of an investment and decreasing in the case of a loan). Compound interest calculates the next interest addition or payment based on the remaining principal.
In the case of a loan, the principal is shrinking over time, as the loan is being paid off.
In the case of an investment, the principal is increasing, as each previous interest payment is added to the principal, ultimately increasing the interest paid after each period.
Most commonly, interest rates are given on an annual basis, while the payment or earnings period is on a monthly basis.
Compounding Other Things Than Money
We have to keep in mind, that the principal can be substituted with any other value, while the interest rate can be substituted with any other growth or decay rate.
This means, that the compound interest formula can be used for other problems than just monetary ones, as long as the following conditions are met.
| Term | Definition |
|---|---|
| Principal | The principal represents a quantitative value of something, which reproduces faster with increasing amounts. |
| Interest rate | The interest rate represents a steady growth or decay rate. |
| Time | There is a clearly defined compounding period. |
Some examples, where this concept can be applied, include population growths of animals, humans, bacteria, etc.
Calculating Compound Interest
In order to successfully calculate the future value (FV), we need to define the following variables:
| Symbol | Definition |
|---|---|
| P | principal, or the present value |
| r | annual interest rate in decimal form, which you get by dividing the percentage by 100 |
| n | number of compounding periods within a year |
| y | number of years |
Then, we can use the following formula.
FV = P * (1+\tfrac{r}{n})^{ny}Do keep in mind, that this formula is a general formula for calculating the future value of an investment with compound interest. It does not consider additional costs, fees, deposits, or withdrawals.
For a more accurate calculation, which includes these variables, use our calculator.
Worked-out Example
What will be the value of $400 invested at a 12% annual compound interest rate for the duration of 5 years? Assume monthly compounding.
First, we define our variables.
| Symbol | Example Value | Note |
|---|---|---|
| P | 400 | as that is the initially invested sum |
| r | 12% | which will be changed to 0.12 in decimal form |
| n | 12 | as the compounding period is monthly, we compound the principal 12 times a year |
| y | 5 | as per instructions |
We substitute these values into the formula.
FV = P * (1+\tfrac{r}{n})^{ny}= 400 * (1+\tfrac{0.12}{12})^{12*5}= 400 * (1+0.01)^{60}= 400 * 1.01^{60}= 400 * 1.8167 = 726.68
The value of the investment will be $726.68 after 5 years.
