What is the formula for simple interest?

What is simple interest?

In simple interest we will learn about how to calculate simple interest. We will recapitulate the formula for simple interest and know more about it. When we borrow money from any source (bank, agency, moneylender), we have to pay back the money after a certain period along with extra money for availing the facility to use the money borrowed.

What is Simple Interest?

● The money borrowed is called the principal (P).

● Extra money paid back is called the simple interest (S.I).

● Interest is expressed as rate par cent per annum (p.a.) i.e., 12% per month means, the interest on $100 for 1 year is $12.

● The total money paid back after the given time is called the amount.

● Time for which money is borrowed is called the time period.

We already know what is simple interest and while calculating the time period we need to:

      Day on which money is borrowed is not counted but the day which the money is returned is counted. 

      When number of day is converted into year, we always divide the number of days by 365, whether it is a leap year or an ordinary year. 

Here, 

P = Principal

R = rate% per annum
T = time
I = simple interest
A = amount
Formula for calculating simple interest is S.I = (P × R × T)/100

Important: Formula for calculating amount is A = P + I

Examples on simple interest:

What is Simple Interest?

1. Find simple interest on $2000 at 5% per annum for 3 years. Also, find the amount.

Solution: 

Principal = $2000

Rate = 5% p.a.

T = 3 years

S.I = (P × R × T)/100

      = (2000 × 5 × 3)/100 

       = $ 300

Amount = P + I

             = $ ( 2000 + 300 )

             = $ 2300

2. Calculate the simple interest on $ 6400 at 10% p.a. for 9 months.

Solution: 

P = $ 6400

R = 10% p.a.

T = 9 months or 9/12 years

[12 months = 1 year

1 months = 1/12 years 

9 months = (1 × 9)/12 years]

Therefore, S.I. = (P × R × T)/100

                        = (6400 × 10 × 9)/(100 × 12)

                        = $480

3. Mike took a loan of $20000 from a bank on 4 February 2009 at the rate of 8% p.a. and paid back the same on 6th July 2009. Find the total amount paid by Mike.

P = $20000

R = 8 % p.a.

T = 152/365

Solution:

Time = February + March +April + May + Jun + July

         = 24 days + 31 days + 30 days + 31 days + 30 days + 6 days

         = 152 days

Therefore, S.I. = (P × R × T)/100

                         = (20000 × 8 × 152)/(100 × 365)

                         = $ (40 × 8 × 152)/73

                         = $ 666.30

Therefore, the amount paid = $ (20,000 + 666.30) = $ 20666.30

What is Simple Interest?

4. At what per cent will $ 1500 amount to $ 2400 in 4 years?

Solution:

P = $ 1500

R = ?

T= 4 years and

A = $ 2400

S.I. = A - P

       = $(2400 - 1500 )

       = $ 900

S.I. = (P × R × T)/100

900 = (1500 × R × 4)/100

Therefore, R = (900 × 100)/(4 × 1500) = 15%

5. In how much time will a sum of money triple itself at 15 % p.a.?

Solution:

Let P = x, then A = 3x

So, I = A - P

         = 3x - x = 2x

We know that S.I = (P × R × T)/100
                                                                                                                                                                     2x = (x × 15 × T)/100

                         T = (2x × 100)/(x × 15) = 40/3 = 13.3 years

6. At what rate percent per annum simple interest will a sum of money double itself in 6 years?

Solution:

Let P = x, then A = 2x

Also, S.I = A - P

               = 2x - x

               = x

T = 6 years

We know that S.I. = (P × R × T)/100

(x × R × 6)/100 = x

R = 100x/6x = 16.6 %

What is Simple Interest?

7. A some amounted to $ 2520 at 10% p.a. for the period of 4 years. Find them sum.

Solution:

Let A = $ 2520

R = 10% p.a.

T = 4 years

P = ?

Let the principal be x

S.I = (x × 10 × 4)/100 = 2x/5

A = P + I

A = x + 2x/5

A = (5x + 2x)/5 = 7x/5 [But given that A = $2520]

7x/5 = 2520

7x = 2520 × 5

x = (2520 × 5)/7 = $ 1800

8. Ron borrowed $ 24000 from his friend at the rate of 12% per annum for 3 years. At the end of the period, he cleared the account by paying $ 10640 cash and giving the cow. Find the price of the cow.

Solution:

Here, P = $24000

R = 12% p.a.

T = 3 years

S.I. = (P × R × T)/100

= (24000 × 12 × 3)/100 = $ 8640

Amount = $24000 + 8640 = $ 32640

Now, $10640 + Price of cow = $ 32460

Therefore, price of the cow = $ 32460 - 10640 = $ 22000

What is Simple Interest?

● Simple Interest

What is Simple Interest?

Calculate Simple Interest

Practice Test on Simple Interest

● Simple Interest - Worksheets

Simple Interest Worksheet

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