Question

Find the sum if The interest paid after 2 year on it is Rs. 550 at the rate of 5% interest per annum at simple interest.​

Answer 1

SOLUTION :-

Given :-

Rate of interest, r = 5%

Period, n = 2 years

Amount, A = Rs. 550

Type of interest = Simple Interest

To find :-

The principal sum = ?

Suppose,

The principal sum = P

We know that,

$\: \: \: \: \: \: \: \: \: \boxed{ \huge{ \sf{ \: S.I. = \frac{P \times r \times n}{100} }}}$

$\: \: \sf{ \therefore \: \: S.I.= \frac{ \: P \times r \times n \: }{100} } \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{ = \frac{ \: P \times 5 \times 2 \: }{100} } \\ \\ \: \: \: \: \: \: \: \: \sf{ = \frac{P \times 0}{100} } \\ \\ \: \: \: \sf{ = \frac{P}{10} }$

According to Question,

$\: \: \: \: \: \: \: \: \: \: \sf{P + S.I. = 550} \\ \\ \sf{ \Longrightarrow \: P + \frac{P}{10} = 550} \: \: \\ \\ \: \sf{ \Longrightarrow \: \frac{10P +P }{10} = 550 } \\ \\ \sf{ \Longrightarrow \: \frac{11P}{10} = 550} \: \: \: \: \: \: \\ \\ \sf{ \Longrightarrow \: 11P = 5500} \: \: \: \: \: \: \\ \\\sf{ \Longrightarrow \: P = \frac{5500}{11} } \: \: \: \: \: \: \: \: \: \\ \\ \sf{ \therefore \: \: P = 500} \: \: \: \: \: \: \: \:$

Hence, the sum is Rs. 500 if the interest paid after 2 year on it is Rs. 550 at the rate of 5% interest per annum at simple interest.

MORE INFORMATION :-

• INTEREST : When a person borrows a sum of money from any financial institution, bank or a person for a period of time, on the expiry of that period, the person has to reoay his debt by paying some extra money along with the original sum of money. The extra money is known as the INTEREST.

• SIMPLE INTEREST : When the interest is calculated on the initial sum borrowed, throughout the specified period, then the interest obtained is known as the SIMPLE INTEREST.

• COMPOUND INTEREST : When the interest that falls due at the end of the specified time is added to the sum borrowed and the amount obtained becomes the Principal for calculating interest for the subsequent period and the process goes on, thus the interest obtained is known as the COMPOUND INTEREST.

• PRINCIPAL : The sum of money which is borrowed by the person is known as the PRINCIPAL.

• AMOUNT : The total money to be paid after a certain period of time taking the Principal and Interest together is known as AMOUNT.

• RATE OF INTEREST : The interest chargedfor one unit of Principal for the period of one year is known as the RATE OF INTEREST.

• PERIOD : The specified time after which the interest is to be paid is known as the PERIOD. It may be one month, three months, six months, one year or two year.

↬ As a general convention, the following notations are used to denote the terms mentioned :

• PRINCIPAL = P

• INTEREST = I

• AMOUNT = A

• RATE OF INTEREST = r

• PERIOD = n

↬ FOMULAS :

$\sf{1)\: \: \: S.I. = \frac{P \times r \times n}{100} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \: \: \: \: \: \: \sf{2) \: \: \: C.I. = \{P (1 + + \frac{r}{100} ) {}^{n} \} -P} \\ \\ \sf{ 3) \: \: \: A = P + I} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf{4) \: \: \: I = A - P} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$