Horje
Difference Between Simple Interest and Compound Interest

Simple interest and compound interest are mainly used in mathematics. Interest can be calculated in two ways: Simple and compound. Simple interest is calculated on principal whereas compound interest is calculated on principal and interest of previous years.

Simple interest and compound interest are widely used in calculating loan repayments and investment growth to savings account explanations or credit card charges. In this article, we will learn about simple interest and compound interest with definitions, formulas, examples, and applications.

Table of Content

Simple Interest

Interest on a loan or investment is traditionally calculated as simple interest, where principal refers to the amount borrowed. Because it does not include the compounding effect, which is clear and simple to follow. Simple Interest Formula:

Simple Interest SI = [P × R × T] / 100

Where:

  • P is the principal amount
  • R is the interest rate per annum
  • T is the time in years

Example

Let us look into and discuss an example to figure out the mechanism of simple interest. Assume the principal amount is $1,000 at 5% interest rate annually for 3 years. Using the formula:

SI = [1000 × 5 × 3] / 100

Therefore, the simple interest earned in 3 years is $150.

Applications

Common uses of simple interest in financial products include:

  • Small-term loans – Primarily used for consumer and personal lending, home mortgages.
  • Savings Account – Some of the savings accounts with banks provide simple interest.
  • Bonds – Interest payments of certain bonds calculated on simple interest

Compound Interest

Compound interest is based on the first principal and also at the added attractiveness of preceding periods. This method of interest compounding will make the investment or loan amount experience exponential growth. The compound interest formula is:

\bf{A~=~P \big(1~+~\frac{R}{n}\big)^{nT}}

Where:

  • A is the amount of money accumulated after n periods, including interest.
  • P is the principal amount.
  • R is the annual interest rate.
  • n is the no. of times interest is compounding per year.
  • T is the time, the money is invested or borrowed for, in years.

Example

Assume principal amount be $1,000 with annually 5% interest compounded annually for the period of 3 years. Using the formula:

A = 1000 \left(1 + \frac{5}{1}\right)^{1 \times 3}

A = 1000 (1 + 0.05)3

A = 1000 × 1.157625

A = 1157.63

Applications

Compound interest is employed in almost every financial product such as:

  • Savings Accounts: Increase savings over time with interest on the principal and compound.
  • Manage investments: Grow wealth exponentially from compounding returns on equities, mutual funds and retirements accounts.
  • Mortage: For mortgages, deal home loan bad debts and expenses within the right way.
  • Retirement Accounts: Future proof income with the reinvested contributions and interest that has grown significantly.

Difference Between Simple Interest and Compound Interest

To learn more about Simple Interest and Compound Interest study the table added below:

Aspect

Simple Interest (SI)

Compound Interest (CI)

Calculation Basis

SI is only calculated on the principal amount.

CI is calculated on the principal amount plus the accumulated interest.

Formula

{SI} = \frac{P \times R \times T}{100}

{A} = P \left(1 + \frac{R}{n}\right)^{nT}

Growth Rate

Linear growth.

Exponential growth.

Interest Earned

Lower interest earned compared to compound interest over the same period.

Higher interest earned due to the compounding effect.

Applications

Short-term loans, some savings accounts, and certain bonds.

Long-term investments, savings accounts, and loans like mortgages.

Example Calculation

For $1,000 at 5% per annum for 3 years:

{SI} = {150}

For $1,000 at 5% per annum for 3 years (compounded annually):

{?} = {1157.63}

Interest Calculation

Interest isn’t added back to the principal amount.

Interest is added back to the principal, leading to compound growth.

Impact if inflation

Less effective in countering inflation.

More effective in countering inflation over time.

Loan Repayment

Repayment amount remains constant over time.

Repayment amount can increase over time with compounding.

Risk Factor

Lower risk due to straightforward calculations.

Higher risk due to variable growth potential.

Problems on Simple Interest and Compound Interest

Problem 1: A takes a loan of $2000 from a bank for a period of 2 year. The rate of interest is 6% per annum. Find the simple interest and the total amount A has to pay.

Solution:

Given,

  • P = $2000
  • R = 6% p.a.
  • T = 2 years

SI = (P × R ×T) / 100

SI = (2000 × 6 ×2) / 100

SI = $240

Total amount that A has to pay to bank

Amount = Principal + Simple Interest

Amount = 2000 + 240

Amount = $2240

Problem 2: B borrowed $6000 from C, for 4 years at the rate of 2.5% per annum. Find the total interest earned by C at the end of 4 years.

Solution:

Given,

  • Principal (P) = $6000
  • Rate of Interest (R) = 2.5 %
  • Time (T) = 4 years

SI = (P × R ×T) / 100

SI = (6000 × 2.5 × 4) / 100

SI = $600

Therefore, the total interest earned by C at the end of 4 years is $600.

Problem 3: What will be the compound interest on $2500 deposited for 2 years, compounded quarterly at interest of 4% per annum.

Solution:

Given,

  • Principal (P) = $2500
  • Rate of Interest (R) = 4%
  • Time (T) = 2 years, compounded quarterly

A = 2500 \left(1 + \frac{4}{4}\right)^{4 \times 2}

A = 2500 (1 + 0.01)8

A = 2500 × 1.082856

A = 2707.14

Compound Interest = 2707.14 – 2500 = 207.14

Problem 4: Find the Compound Interest when principal = $1500, rate = 5% per annum compounded annually and time = 3 years.

Solution:

Given,

  • Principal (P) = $1500
  • Rate of Interest (R) = 5%
  • Time (T) = 3 years, compounded annually

A = 1500 \left(1 + \frac{5}{1}\right)^{1 \times 3}

A = 1500 (1 + 0.05)3

A = 1500 × 1.157625

A = 1736.44

Compound Interest = 1736.44 – 1500 = 236.44

FAQs on Simple Interest and Compound Interest

What is Simple Interest?

Simple Interest calculates interest on the principal amount and it does not accumulate any previous cycle earned an interest over to next.

What is Compound Interest?

Compound Interest is the type of amount which computed on both the principle and previous earned benefits over time in a certain discipline.

What is Simple Interest Formula?

{SI} = \frac{P \times R \times T}{100}

What is Compound Interest Formula?

A = P \left(1 + \frac{R}{n}\right)^{nT}

Why Does Compound Interest Grow Much Faster Than Simple Interest?

Compound interest yield grows exponentially, and simple interest yield only increases on a linear basis.

Why Compound Interest is Ideal for Long-term Investments?

Compound interest is good for long-term investments because the investor/customer gets the interest paid on both the invested principal value and the interest earned in previous intervals.

Conclusion

Simple interest and compound interest basics is necessary for taking better money decisions. Simple interest is simple to calculate and typically adds or subtracts a fixed amount of money, while compound interest can grow the balance or final payment by much more over time due to compounding. Must know for students and those into financial planning which helps in understanding the different type of financial product evaluation to make a superior choice with respect of an investment.


 


Reffered: https://www.geeksforgeeks.org

Mathematics

Related
Comparing Ordinal and Continuous Data Comparing Ordinal and Continuous Data
Division of a Line Segment Practice Problems Division of a Line Segment Practice Problems
Degrees and Radians Conversion Worksheet Degrees and Radians Conversion Worksheet
Rational Expression: Definition, Example & Simplification Rational Expression: Definition, Example & Simplification
Real Life Applications of Cartesian Product Real Life Applications of Cartesian Product

Type:
 Geek
Category:
 Coding
Sub Category:
 Tutorial
Uploaded by:
 Admin
Views:
 21



 

Horje