The Difference of Compound Interest and Simple Interest is explained based on the principal amount. The simple interest depends on the principal amount and compound interest depends on the principal amount and the interest compounded for a cycle of the period.

These Compound Interest and Simple Interest concepts are mainly used in banking and financial services. Loans like educational loans, auto loans, and mortgages use simple interest. Compound interest is mostly used by the saving accounts as it pays the interest. To know deeply about simple interest and compound interest, check out the 10th Grade Math articles.

Read More About

- Compound Interest as Repeated Simple Interest
- Compound Interest with Periodic Deductions
- Compound Interest with Growing Principal

## Definition of Compound Interest and Simple Interest

The definitions of the compound and simple interests are given below.

**Compound Interest:** The Compound Interest is the interest of the compounds over the principal amount.

**Simple Interest:** The Simple Interest is the interest where the principal amount of a deposit, or a loan that a person makes into their bank account.

### Difference Between Simple Interest and Compound Interest in Tabular Form

The below table will let you understand deeply the difference between Compound Interest and Simple Interest.

Parameter | Compound Interest | Simple Interest |
---|---|---|

Definition | Compound Interest is defined as the sum of the principal amount is exceeds the due date of payment along with the rate of interest for a particular period of time. | Simple Interest is defined as the sum paid back for the borrowed money, over a fixed period of time. |

Formula | C.I. = P(1+R⁄100)^{t} − P |
S.I. = (P × T × R) ⁄ 100 |

Principal Amount | The principal amount will vary in the entire borrowing period. | The principal amount is constant in Simple Interest |

Return Amount | It is higher in compound interest | It is lower compared to compound interest |

Interest Charged | The interest is charged for the principal and accumulated interest. | The interest is charged for the principal amount. |

Growth | It increases quite rapidly. | It is quite uniform. |

**Note:** If the rate of interest per annum is the same for both compound interest and simple interest, then for 2 years, compound interest (CI) – simple interest (SI) = Simple interest for 1 year on “Simple interest for one year”.

### Difference between Compound Interest and Simple Interest Examples with Solutions

We have given different examples of the difference between Compound Interest and Simple Interest.

**Question 1.**

Find the difference between the compound interest and simple interest on $ 30,000 at the same interest rate of 8 % per annum for 2 years.

**Solution:**

Given that the principal amount or the initial amount = $30000

Rate of interest = 8% per annum

Number of years the amount is deposited or borrowed for (t) = 2 years

Firstly, find the simple interest.

The formula to find the simple interest is (P × T × R) ⁄ 100 where p is the principal amount, R is the Rate of interest, and T is the time period.

Substitute all the information in the above formula.

Simple interest = (30000 × 2 × 8) ⁄ 100 = 4800

Therefore, the Simple interest for 2 years = 4800

Now, find the compound interest.

The formula to find the compound interest is C.I. = P(1+R⁄100)^{t} where p is the principal amount, R is the Rate of interest, and T is the time period.

Substitute all the information in the above formula.

C.I. = 30000(1 + 8⁄100)^{2}

C.I. = 30000(108⁄100)^{2} = 30000(27⁄25)^{2} = 30000 * (27⁄25) * (27⁄25) = 34992.

Therefore, the compound interest for 2 years = 34992

Thus, the required difference of the compound interest and simple interest = 34992 – 4800 = $30192.

**Question 2.**

What is the sum of money on which the difference between simple and compound interest in 2 years is $ 150 at the interest rate of 2% per annum?

**Solution:**

Let the principal amount or the initial amount = $a.

Rate of interest = 2% per annum

Number of years the amount is deposited or borrowed for (t) = 2 years

Firstly, find the simple interest.

The formula to find the simple interest is (P × T × R) ⁄ 100 where p is the principal amount, R is the Rate of interest, and T is the time period.

Substitute all the information in the above formula.

Simple interest = (a× 2 × 2) ⁄ 100 = a/25.

Therefore, the Simple interest for 2 years = a/25

Now, find the compound interest.

The formula to find the compound interest is C.I. = P(1+R⁄100)^{t} where p is the principal amount, R is the Rate of interest, and T is the time period.

Substitute all the information in the above formula.

C.I. = a(1 + 2⁄100)^{2}

C.I. = a(102⁄100)^{2} = 30000(51/50)^{2} = a * (51/50) * (51/50) = 2601a/2500.

Therefore, the compound interest for 2 years = 2601a/2500

Thus, the required difference of the compound interest and simple interest = 2601a/2500 – a/25 = $ 150.

a = 149.940

Therefore, the principal amount is $149.940.

**Question 3.**

Find the difference between the compound interest and simple interest on $ 50,000 at the same interest rate of 6 % per annum for 2 years.

**Solution:**

Given that the principal amount or the initial amount = $50000

Rate of interest = 6% per annum

Number of years the amount is deposited or borrowed for (t) = 2 years

Firstly, find the simple interest.

The formula to find the simple interest is (P × T × R) ⁄ 100 where p is the principal amount, R is the Rate of interest, and T is the time period.

Substitute all the information in the above formula.

Simple interest = (50000 × 2 × 6) ⁄ 100 = 6000

Therefore, the Simple interest for 2 years = 6000

Now, find the compound interest.

The formula to find the compound interest is C.I. = P(1+R⁄100)^{t} where p is the principal amount, R is the Rate of interest, and T is the time period.

Substitute all the information in the above formula.

C.I. = 50000(1 + 6⁄100)^{2}

C.I. = 50000(106⁄100)^{2} = 50000(53/50)^{2} = 50000 * (53/50) * (53/50) = 56180.

Therefore, the compound interest for 2 years = 56180

Thus, the required difference of the compound interest and simple interest = 56180 – 6000 = $50180.

### FAQs on What is the Difference between Compound Interest and Simple Interest

**1. What is the main difference between compound interest and simple interest?**

Compound interest is calculated based on the principal amount as well as the interest accumulated for a certain period or previous period whereas simple interest is calculated based on the loan amount or principal amount.

**2. What is the formula for the amount if it is compounded annually?**

The formula to find the amount if it is compounded annually is **P(1+R⁄100) ^{t}**

- where p is the principal amount,
- R is the Rate of interest, and
- T is the time period.

**3. What is the formula for Simple interest?**

The formula to find the simple interest is **(P × T × R) ⁄ 100**

- where p is the principal amount,
- R is the Rate of interest, and
- T is the time period.

**4. What is the formula for compound interest?**

The formula to find the compound interest is CI = Amount – Principal.

Amount = P(1+R⁄n)^{nt}.

### Conclusion

Hope you have found the major differences between Compound Interest and Simple Interest by reading the entire article. Finding the time period, rate of interest, the principal amount is easy by understanding the concepts of compound interest, and simple interests on our website.