Notes on Simple Interest | Grade 8 > Compulsory Maths > Simple Interest | KULLABS.COM

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Interest is a profit of an investment. There are many ways to calculate the interest. The quick method of calculating the interest charge on a loan is called simple interest. The sum of money invested is called the principal which is denoted by 'P'. The money earned by the principal is called the interest (I) and is earned at a rate known as the interest rate (R).

Example

Let us consider an investment on simple interest terms of Rs 200 invested for 2 years at 15% per annum ( p.a). Each year the investor will receive interest equal to 15% of the principal. Interest received at the end of the first year = 15% of Rs 200 = $$\frac{15}{100}$$x 200 = Rs.30

Similarly, interest received at the end of the second year = Rs 30.

The total interest ( I ), received = Rs 30 + Rs 30 = Rs 60

The investor also gets the principal of Rs 200 back at the end of the second year.

In the above example, interest ( I ) = 15 % of Rs 200 x 2

Interest ( I ) = 15 % of Rs 200 x 2

= $$\frac{15}{100}$$x 200 x 2

Replace, $$\frac{15}{100}$$ by R, Rs 200 by P and 2 by T

I = R x P xT

Thus, I = PTR

Hence, if Rs P is invested at the rate of R% per annum for T years, then the interest, Rs I, earned is given by I = PTR

Also, P = $$\frac{I}{TR}$$, T = $$\frac{I}{PR}$$ and R = $$\frac{I}{PT}$$

The sum of principal and interest is called amount ( A )

Thus, A = P + I

A = P +PTR

A = P (1 + TR )

So, P = $$\frac{A}{1+TR}$$

Examples

1. Sabina borrowed Rs 2,000 for 2 years at 10% interest rate. How much interest will she pay at simple interest?
Solution:
Principal (P) = Rs.2,000
Rate (R) = 10% = $$\frac{10}{100}$$ p.a
Time (T) = 2 years
We have,
Simple interest (I) = P × T × R
= Rs.2000 × 2 × $$\frac{10}{100}$$
= Rs.400
$$\therefore$$ Sabina will pay Rs.400 as interest.

2. Tripti borrowed Rs 10,000 at a rate of 15 % p.a. for 6 months. How much simple interest did she pay?
Principal (P) =Rs 10,000
Rate (R) = 15 % p.a. = $$\frac{15}{100}$$ p.a
Time (T) = 6 months =$$\frac{6}{12}$$years
W e have,
Simple Interest (I) = P × T × R
= Rs.10,000 ×$$\frac{6}{12}$$ ×$$\frac{15}{100}$$
= Rs.750
$$\therefore$$ Tripti paid Rs.750 as interest.

• Simple interest is a quick method of calculating the interest charge on a loan.
• Simple interest is determined by multiplying the interest rate by the principal by the number of periods.
• The sum of money invested is called the principal which is denoted by ' P '.
• The money earned by the principal is called the interest (I) and is earned at a rate known as the interest rate (R).
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### Very Short Questions

Solution,

Given information,

Principal amount (P)= Rs 76,00

Time (T) = 3 years

Interest (I) = Rs 1,254

Rate (R) =?

Formula, R = $$\frac{I×100}{PT}$$

(R) = $$\frac{1254×100}{7600×3}$$

= 5.5%

Solution:

Given information,

Time (T) = 7 years

Interest (I) =Rs 4200

Rate (R) = 6%

Principal (P) = ?

Formula, P= $$\frac{I×100}{TR}$$

∴ (P) = $$\frac{4200×100}{7×6}$$

= $$\frac{420000}{42}$$

= Rs 10,000

∴ She has to Rs 10,000 now.

Solution:

Given inforamtion,

Principal (P) = Rs 3,000

Rate (R) = 5% = $$\frac{5}{100}$$ p.a

We have,

Simple Interest (I) =P× T× R

= Rs 3,000× 4× $$\frac{5}{100}$$

=Rs 600

Hence , She will pay Rs 600 at simple interest.

Solution:

Given information,

Principal(P) = Rs 12,000

Rate (R) = 18% = $$\frac{18}{100}$$ p.a

Time (T) = 9 Months = $$\frac{9}{12}$$ years

We have,

Simple Interest (I) = P× T× R

= Rs 12,000× $$\frac{18}{100}$$× $$\frac{9}{12}$$

= Rs 1,620

So, Suzu paid Rs 1,620 in interest.

Solution:

Given information,

Principal (P) = Rs 3000

Since, we are doubling Rs 3000, we made an additional Rs 3000 on this investment, which is the interest.

So, Interest (I) = Rs 3000

Rate (R)= 20% = $$\frac{20}{100}$$ p.a

We have,

Time (T) = $$\frac{3000}{3000 \times \frac{20}{100}}$$

= $$\frac{100}{20}$$

Hence, It takes 5 years to double the amount.

Solution:

Given information,

Time (T) = 2 Years

Simple Interest (I) = Rs 100

Rate (R) = 8% =$$\frac{8}{100}$$

We have,

P = $$\frac{I}{T×R}$$

= $$\frac{100}{2\times\frac{8}{100}}$$

= $$\frac{10000}{16}$$

= 625

Hence, principal is Rs 625

Solution:

Given information,

Principal (P) =Rs 100

Interest (I) =Rs 200

Time (T) = 3 years

We have,

R = $$\frac{I}{P×T}$$

= $$\frac{200}{100×3}$$

= $$\frac{200}{300}$$

= 66%

Hence, The interest rate is 66%

Solution:

Given Information,

Rate (R) =2%

Time (T) = 3 years

Interest (I)= Rs 120

Principal (P) = ?

We know ,

P =$$\frac{I×100}{T×R}$$

= Rs $$\frac{120×100}{T×R}$$

= Rs 2000

∴ Rs 2000 amount should be invested.

Solution:

Given information,

Principal (P) = Rs 1500

Time (T) = 4 years

Interest (I) = Rs 200

Rate (R) =?

We know,

Interest Rate (R) = $$\frac{I×100}{P×T}$$

= $$\frac{I×100}{1500×4}$$

=$$\frac{50}{15}$$

=$$\frac{10}{3}$$%

= 3 $$\frac{1}{3}$$ %

∴ Interest Rate (R) = 3 $$\frac{1}{3}$$ %

Solution:

Given information,

Principal(P)= Rs 7,200

Time (T) = 5 Years

Interest(I) = Rs 1080

Interest Rate(R) = ?

We know,

R = $$\frac{I\times100}{PT}$$

= $$\frac{1080\times100}{7100\times5}$$

Hence, Interest Rate(R) = 3%

0%

4Years
5 Years
9 Years
7 Years

9%
11%
7%
8%

Rs 60
Rs 70
Rs40
Rs 50

Rs 20
Rs 27
Rs 18.38
Rs 25

Rs 15,000
Rs 12,000
Rs 10,000
Rs 16,000

Rs 55
Rs 60
Rs 45
Rs 50

7%
5%
10%
6%

Rs 1000
Rs 1500
Rs 1200
Rs 1170

Rs 325
Rs 350
Rs 200
Rs 205

Rs 30,000
Rs 35,000
Rs 40,000
Rs 45,000

Rs 55,000
Rs 65,000
Rs 60,500
Rs 50,000

Rs 1500
Rs 1250
Rs 1000
Rs 1200

Rs 50
Rs 40
Rs 45
Rs 55

11 Years
5 Years
8 Years
7 Years

Rs 50,000
Rs 60,000
Rs 55,500
Rs 65,000

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##### Drishya

Find the rate of interest if Rs 4000 amounts to Rs 6000 in 2 years