Note on Simple Interest

  • Note
  • Things to remember
  • Exercise
  • Quiz

.

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).
.

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%
  • Find the value (T) Time:

    Principal(P) =Rs 1250

    Rate(R) = 13%

    Interest(I) = Rs 650

    Time(T) =?

    5 Years
    9 Years
    4Years
    7 Years
  • Find the value of  Interest Rate(R)?

    Principal(P) = rS 1460

    Time(T) = 30 Months

    Interest(I) = Rs 292

    Rate =?

    9%
    7%
    11%
    8%
  • Find the difference between compound interest and simple interest on Rs 12,000 and in 1(frac{1}{2}) years at 10% compounded yearly.

    Rs 60
    Rs40
    Rs 70
    Rs 50
  • Saroj invested Rs 8,000 for 3 years at a simple interest rate of 8% per annum. He also  invested the same sum for the same period at a compound interest rate of 7(frac{1}{2})% per annum, how much more would he have received after 3 years?

    Rs 27
    Rs 25
    Rs 18.38
    Rs 20
  • Find the sum of money invested, if the difference between the compound interest and simple interest for 2 years at 9% per annum is Rs12960.

    Rs 16,000
    Rs 15,000
    Rs 12,000
    Rs 10,000
  • Calculate the simple interest on Rs 600 for 2(frac{1}{2})years at 4% per annum.

    Rs 55
    Rs 50
    Rs 45
    Rs 60
  • Renu took Rs 400 from Saroj and returned him Rs 3000 after 5 years. Find the annum rate of interest in percent.

    7%
    5%
    10%
    6%
  • What will be the amount on Rs 900 at 5 % per annum for 6 years?

    Rs 1000
    Rs 1200
    Rs 1170
    Rs 1500
  • Sapana  took a loan of Rs  850 from Renu  for 3 years at 10 % per annum. After 3 years Sapana paid back the loan by giving Rs 900 in cash and a New Bag. What was the price of the New Bag?

     

    Rs 200
    Rs 205
    Rs 325
    Rs 350
  • What is the  difference between the compound interest and simple interest for 3 years that become Rs  930 at 10%.

    Rs 40,000
    Rs 45,000
    Rs 30,000
    Rs 35,000
  • Find the Amount (A)?

    Principal(P) = Rs 50,000

    Time(T) =7 Years

    Rate (R) =3%

    Amount(A) = ?

    Rs 65,000
    Rs 50,000
    Rs 60,500
    Rs 55,000
  • Find the Principal (P).

    Rate (R) = 9%

    Time (T) = 9 Years

    Interest (I) = Rs 810

    Principla =?

    Rs 1250
    Rs 1500
    Rs 1200
    Rs 1000
  • Find the Simple Interest of the following?

    Principal(P)=Rs 500

    Rate (R) = 3%

    Time (T) = 3 Years

    Simple Interest (S.I) =?

    Rs 45
    Rs 50
    Rs 55
    Rs 40
  • Find the value of Time (T)?

    Principal (P) = Rs 4500

    Rate (R) = 4%

    Interest (I) = Rs 900

    Time (T) =?

    7 Years
    8 Years
    11 Years
    5 Years
  • To get Rs 56,610 in 4 months, how much amount should be invested now at the rate of 6 %?

    Rs 55,500
    Rs 65,000
    Rs 50,000
    Rs 60,000
  • You scored /15


    Take test again

DISCUSSIONS ABOUT THIS NOTE

You must login to reply

Forum Time Replies Report


You must login to reply

Krishna deposited Rs 60000at the rate of 8% in saving. After 5 years he withdrew Rs.40000 and total interest of 5 years. How long should he keep the remaining amount to get total interest Rs. 28800 from the beginning?

Plz do this?


You must login to reply

Drishya

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


You must login to reply

PRINCIPLE= 10921

PRI


You must login to reply