## Difference Between Simple and Compound Interest

Simple interest refers to the interest which is calculated on principal amount that is borrowed or invested by the person whereas compound interest refers to the interest which is calculated on principal amount that is borrowed or invested by the person along with the previous period’s accumulated interests.

Interest is the fees paid by the borrower to the lender for borrowing money. For example, banks charge interest on the loans taken by the customers. People deposit money in the banks to earn interest on the amount deposited. Higher interest rates higher is the opportunity for investors to earn higher rates of return.

There are two ways to calculate the interest on the principle: Compound and the Simple interest.

### What is Simple Interest?

Simple interest as the name suggests is simple in the calculation and to understand. It is the amount that the lender charges the borrower on only the principal loan.

The formula to Calculate Simple Interest is:

Where SI is Simple Interest

- P is Principal
- R is the rate
- And T is the time for which the loan is given

The amount owed at the end of the period is given by

A = SI + P or A = PRT/100 + P

### What is Compound Interest?

Compound interest is the interest earned on the principal amount as well as the interest earned on the accrued interest. Compound interest depends on the frequency of compounding i.e. the interest can be compounded daily, monthly, quarterly, half-yearly or annual, etc.

The formula to calculate amount earned when the principal is compounded is given as:

Where A is the Amount,

- P is the principal,
- R is the rate of interest
- T is the time for which the principal is owed

Thus, the Compound Interest is calculated = A – P = P (1 + r/100)^{T} – P

It can be equal to or more than the simple interest depending on the time and frequency of compounding.

### Simple Interest vs Compound Interest Infographics

### Examples

Let us understand compound interest and simple interest with examples.

#### Example #1

Consider a person XYZ who keeps $ 1000 in a bank for a period of 1 year at a 5% interest rate. Calculate the Simple and compound interest (compounded annually)?

**Simple Interest** = P * R * T/100

- SI = 1000 * 5 * 1/100
- SI = $ 50

**Compound Interest** = P (1 + r/100)^{T} – P

- CI = 1000 (1 + 5/100)
^{1}– 1000 - CI = $ 50

Here, since the interest is compounded annually and the duration of the deposit is 1, both the interest are equal.

#### Example #2

Now, let us consider the same example and change the duration to 2 years.

**Simple Interest** = P * R * T/100

- SI = 1000 * 5 * 2/100
- SI = $ 100

**Compound Interest** = P (1 + r/100)^{T} – P

- CI = 1000 (1 + 5/100)
^{2}– 1000 - CI = 1102.5 – 1000 = $ 102.5

Thus, with the change in the duration of the deposit the interest earned has increased by $ 2.5. This, $ 2.5 is basically the interest earned on the interest accumulated in the first year of deposit.

### Key differences

Key Differences are as follows –

- Simple interest is interest only on the principal whereas compound interest is the interest earned on the principal and the subsequent interest accumulated overtime period
- The principal amount remains the same in simple interest whereas the principal amount changes as the interest are accumulated over the period of time
- Simple interest does not depend on the frequency of the interest calculation where compound interest depends on the frequency; the compound interest is higher when the frequency increase.
- Compound interest is always higher than or equal (only if compounded annually and for a term of 1 year) to the simple interest.
- Simple interest has lesser returns to the investor than the compound interest.
- Wealth creation is more when the principal is compounded than if simple interest is used.
- The final amount after the period ends in a simple interest is given by P(1 + RT/100) whereas the final amount in Compound interest is P (1 + r/100)
^{T} - The interest earned when it is simple interest is calculated as P * R * T/100 whereas when the interest is compound the interest earned is P((1 + r/100)
^{T}– 1).

### Simple vs Compound Interest Comparative Table

Basis |
Simple Interest |
Compound Interest |
||

Definition |
Simple Interest is earned only on the principal amount | It is on the principal as well as the interest accrued over time | ||

Amount of interest earned |
The amount of interest earned is small and leads to lesser wealth growth | The amount of interest earned is higher and wealth growth increases as the interest are earned on the accumulated interest in the previous periods | ||

Returns on principal |
Fewer returns as compared to compound interest | Higher returns than the simple interest due to compounding | ||

Principal |
The principal remains the same during the tenure | Principal increases as interest are compounded and are added to the original principal | ||

Calculation |
It is easy to calculate | It is bit complex in calculation than simple interest | ||

Frequency of Interest Rate |
Does not depend on the frequency of interest accumulation | It depends on the frequency of interest calculation and the amount increases if the frequency increases | ||

Formula |
P * R * T/100 | P (1 + r/100)^{T} – P |
||

Amount Earned After Duration |
P * R * T/100 + P | P (1 + r/100)T |

### Recommended Articles

This has been a guide to Simple vs Compound Interest. Here we discuss the top difference between them along with infographics and comparison table. You may also have a look at the following articles –

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