[Maths Class Notes] on Interest Pdf for Exam

Interest is the amount of money paid for the use of other’s money. When you borrow money from lenders, you pay interest. When you lend money to borrowers, you get interest. It may be expressed either in monetary terms or rate of payment.

Here, you will learn, what is interest in detail including the types of interest, interest definition, and how to calculate the interest amount on the amount borrowed or lent.

What is an Interest?

Interest is an additional amount of money that is paid by the borrower to a lender or an investor beyond reimbursing the amount borrowed. For example, a borrower may borrow [$]20000 and agree to pay [$]200 in interest above and beyond the amount owed. An interest rate is the amount of interest paid or interest received over a specified period. For example, if the previous borrower agrees to repay the amount owed in one year’s time, then the interest rate is 10%.

Interest can be simple meaning calculated the interest amount once on the principal overdue or compounded meaning calculated the interest amount on the principal overdue plus the interest accrued. And compound interest can be calculated daily, monthly, half-yearly, quarterly or even annually.

Albert Einstein reportedly said, “compound interest is the most powerful force in the universe”.It implies that investment can grow to an unlimited amount over time or debt can be accumulated to an unmanageable level because of the compound interest.


How Does Interest Work?

There are several ways to calculate the interest, and some methods to calculate interest are more beneficial for lenders. The amount of interest you pay relies on what you expect to get in return whereas the amount of interest you get relies on the alternative investment options available for investing your money.

When Borrowing – When you borrow money, you need to repay what you borrowed. To compensate the lender for the risk of lending money, you need to repay more you borrowed in the form of interest.

When Lending – If you have extra funds, then you lend it out or deposit the extra funds in the savings account, enabling the bank to lend it out or invest the available funds. In return, you expect to earn interest on the amount you lend or deposit.

Amount of interest you pay or earn relies on the following factors:

A higher rate of interest or long term loans results in the borrower paying more interest.

For Example, An interest rate of 10% per year and a loan of [$]100 results in an interest charge of [$]10 per year assuming you use a simple interest formula to calculate your interest amount. Most credit card issuers and banks do not use simple interest, rather they use compound interest, resulting in an interest amount to grow more rapidly.

Let us learn more about how to calculate interest using simple interest and compound formulas.

How to Calculate Interest?

Interest can be calculated using two methods. These two methods:

  1. Simple Interest

  2. Compound Interest

Let us discuss the methods of calculating the interest in detail.

What is Simple Interest?

Simple interest is a method of calculating interest either on the amount borrowed or invested for the entire period of the loan without considering any additional factors such as past interest ( paid or charged) or any other financial consideration. Simple interest is paid on the original principal amount, it is not compounded. Generally, simple interest is applied to a short term loan, usually one year or less, that is managed by financial companies or money invested for a similar short term duration.

The formula for calculating simple interest is

Simple Interest ( SI) = P × R × T / 100

Here, P is the principal amount, R is the rate of interest, T is the time period of interest.

The final amount to be paid is the principal amount plus the simple interest i.e. P + SI.

For example,

Q. An invested sum fetched a total interest of $5000 at the rate of 10% in one year. What was the original principal amount?

Solution: Let principal amount be P, SI be simple interest, R be the rate of interest, and T the time period.


SI = PRT/100

5000 = P × 10 × 1

P = 5000/10

P = 500

Hence, the original principal amount is [$]500.

Compound Interest

Generally, interest rates on investments and loans are compound interest, the interest is not calculated on the original principal but is calculated on the amount invested or owed at the time of calculation. In this way, interest is said to be compounded. Compound interest is beneficial for the investor as it enables them to generate more return, not only their original principal amount.

Compound interest is basically defined as the interest which is charged on another interest. If I take a loan of [$]2000  annually such that the interest rate is 10%, then the interest for the first year would be 10% of [$]2000 i.e. [$]200. The principal amount for the second year will be 2000 + 200 = [$]2200. Accordingly, the interest in the second year will be 10% of [$]2200 = [$]220.

Hence, we can see that compound interest is the interest charged on another interest.

Compound Interest Formula

The formula for calculating the amount received when interest is compounded annually:

Amount = Principal (1 + Rate/100)

The total compounded interest over the term is calculated as

Compound Interest = Amount – Principal

Solved Example

1. In how many years will an amount of [$]2000 will be doubled, if the interest rate is 10% per annum?

Solution: Let the principal amount be P, R be the rate of interest per annum, SI be simple interest, and T be the time period.


SI = PRT/100

2000 = 2000 × 10 × T ( because SI = P)

T = 20000/ 2000

T = 10 years

Hence, the amount of Rs.1000 will be doubled in 10 years.

2. What would be the amount Rs.100 in a year if the interest rate is 10% half-yearly ( every 6 months).

Solution: Let A be the amount received,  P be the principal amount, R be the rate of interest per annum, SI be simple interest and T be time period.


A = P (1 + R)T

= 100 × (1 + 10/100

= 100 × (21/< /span>20

= 100 × ( 441/400

= 441/4

= 110.25

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