Financial Modeling Tutorials

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- Simple Interest
- Simple Interest vs Compound Interest
- Simple Interest Formula
- CAGR Formula (Compounded Annual Growth Rate)
- Effective Interest Rate
- Loan Amortization Schedule
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- Interest Rate Formula
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- Rule of 72
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- Opportunity Cost Formula
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- Mortgage APR vs Interest Rate
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- Coefficient of Variation Formula
- Sample Standard Deviation Formula
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- Binomial Distribution Formula
- Quartile Formula
- P Value Formula
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- R Squared Formula
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- Regression vs ANOVA
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- F-Test Formula
- Quantitative Research

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## Compound vs Simple Interest

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

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

In this article we will discuss both the **Simple interest vs Compound Interest**, we will look into a head on the head comparison and the key differences between the two types of interest rate calculations.

### What is Simple Interest?

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

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

4.9 (927 ratings)

### 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

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

### Compound Interest vs Simple Interest Infographics

Here we provide you with the Infographics of Compound Interest vs Simple Interest

### Simple Interest vs Compound Interest Examples

Let us understand Compound Interest vs Simple Interest with examples

#### Example #1

Consider a person XYZ keeps $ 1000 in a bank for a period of 1 year at 5% interest rate. Calculate the Simple interest vs 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 Simple Interest vs Compound 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.

### Compound Interest vs Simple Interest Key differences

Key Differences between Simple Interest vs Compound Interest

- 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
- Simple interest is easy to calculate whereas compound interest is bit complex
- 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 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/100where as when the interest is compound the interest earned is P((1 + r/100)
^{T}– 1)

### Compound Interest vs Simple Interest Head to Head Difference

Let’s now look at the head to head comparison Between Simple Interest vs Compound Interest

Basis – Simple Interest vs Compound Interest |
Simple Interest |
Compound Interest |
||

Definition |
Simple Interest is earned only on the principal amount | Compound interest 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 precious periods | ||

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

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

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

The 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 | ||

The formula for calculation of interest |
P * R * T/100 | P (1 + r/100)T – P | ||

Amount earned after the duration |
P * R * T/100 + P | P (1 + r/100)T |

### Recommended Articles

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

- Definition of Compound Journal Entry
- Formula of Daily Compound Interest
- What is Accrued Interest?
- Money vs Currency | Differences (with Infographics)
- Interest vs Dividend | Differences (with Infographics)
- Calculate Interest Income
- Inflation vs Interest Rate Differences
- Imputed Interest Formula

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