Simple Interest

Simple Interest

When interest is calculated for every term on same Principal at same rate and added at the end of time period, the sum is called Simple Interest (SI). Simple Interest is added to the Principal to calculate the Amount at the end of time period for which money is borrowed.

Interest

Borrowed money has to be returned at the end of time period with some extra money. This extra money is called Interest.

Principal

Borrowed money is called Principal.

Time Period

Period of time for which money is borrowed is called time period.

Rate of interest

Interest is charged as some percentage of Principal per term of the time period. When the rate is charged yearly it is called rate per annum.
e.g., 10% per annum, which means 10% of the principal will be charged as interest per year of the time period.

Amount

Sum of Principal and Interest to be returned after the given period of time is called Amount.

Interest for one year

● When money is borrowed for one year of time period at the rate of R% annually.
Interest = R% of Principal
= \frac{R}{100}\times P = \frac{P\times R}{100}

Q) Rs 10,000 is invested at 5% interest rate p.a. Find the interest at the end of one year.
A) P = Rs 10,000
R = 5% p.a.
Interest at the end of year = R % of P

=\frac{P\times R}{100}= \frac{10000\times 5}{100} = Rs \,500

Interest for multiple years

Money is borrowed for more than one year of time period .

SIMPLE INTEREST

When interest is calculated for every term on same Principal at same rate and added at the end of time period, the sum is called Simple Interest (SI).
SI for one year at R% per annum = \frac{P\times R}{100}

SI for two years = \frac{P\times R}{100} + \frac{P\times R}{100} = \frac{2\times P\times R}{100}

SI for T years = \frac{P\times R}{100} + \frac{P\times R}{100}\cdots T times = \frac{P\times R \times T}{100}

Amount (A) payable after T year = P + SI

Formula for Simple Interest

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

\boxed{A = P + SI}

Where,
P = Principal borrowed on interest
R = Rate of interest per annum
T = Time Period in years
SI = Simple Interest to be paid after T years
A = Amount to be paid aftet T years.

Try These

(Q1) Rs 3,500 is given at 7% p.a. rate of interest. Find the interest which will be received at the end of two years
(Q2). Rs 6,000 is borrowed at 6 % rate of interest p.a.. Find the interest and the amount to be paid at the end of 3 years.
(Q3). You have Rs 2,400 in your account and the interest rate is 5%. After how many years would you earn Rs 240 as interest.
(Q4). On a certain sum the interest paid after 3 years is Rs 450 at 5% rate of interest per annum. Find the sum.

(A1) P = 3,500
R = 7% p.a.
T = 2 years
∴ SI =\frac{ P\times R\times T}{100} = \frac{ 3500 \times 7\times 2}{100} = Rs 490

(A2) P = 6,000
R = 6% p.a.
T = 3 years
∴ SI =\frac{ P\times R\times T}{100} = \frac{ 6000 \times 6\times 3}{100} = Rs 1080

(A3) P = 2,400
R = 5% p.a.
SI = Rs 240
T = ?
∵ SI = \frac{ P\times R\times T}{100}
\implies 240 = \frac{2400\times 5\times T}{100}
\implies 240 = 24\times 5\timesT
\implies 24\times 5\times T = 240
\implied T = \frac{240}{24\times 5} = 2 years
∴ After 2 years we would earn Rs 240 as interest.

(A4) P = ?
R = 5% p.a.
SI = Rs 450
T = 3
∵ SI = \frac{ P\times 5\times 3}{100}
\implies 450\times 100 = 15\times P
\implies 15\times P = 450\times 10p
\implied P = \frac{4500}{15} = 3000
∴ The sum borrowed = Rs 3000.

 

Percentage
Compound Interest

 

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