Simple Interest - Arithmetic

Important Terms and Formula related to simple interest

Simple Interest (SI) = Principal (P) × Rate (R) % × Time (T)

Amount (A) = Principle (P) + Interest (I)

Where S.I. = Simple Interest, P = Principal or Sum, and T = Time

Principal (P) : The money borrowed is known as Principal (P) or Sum

Time (T) : The period for which the money is borrowed is called Time. Generally, time is fixed in years.

Interest : The extra amount pays on money borrowed for a certain time period, is called the Interest. Interest is generally denoted in percent per year.

Simple Interest (S.I.) : If extra money to paid on the amount borrowed is reckoned uniformly, then it is called the Simple Interest. In the case of simple interest, the interest is not added with the principal amount to reckon interest further on it.

Amount (A) : The sum of Principal and Interest is called the Amount. Amount is generally denoted by letter "A"

Questions on Simple Interest and their solution using forumula and Unitary Method

Question (1) Calculate the simple interest on a sum of $1000 at the rate of 5% per annum for 1 years.

Solution

Given, Principal or Sum (P) = $1000

Time (T) = 1 year

Rate (R) = 5% per annum

Thus, Simple Interest (SI) = ?

We know that, SI = PRT

= $1000 × 5% × 1

= $10 × 5 × 1

⇒ SI = $50

Thus, simple interest = $50 Answer

Alternate method (Unitary Method) to calculate the Simple Interest (SI)

Given, Principal or Sum (P) = $1000

Time (T) = 1 year

Rate (R) = 5% per annum

Thus, Simple Interest (SI) = ?

Here, rate 5% per annum.

This means $5 will be the interest on $100 for one year.

Now, since on $100 the simple interest for one year = $5

∴ on $1, the simple interest for one year

∴ on $1000, the simple interest for one year

Thus, on $1000 the simple interest for 1 year = $ 50 Answer

Question (2) Calculate the simple interest on a principal of $500 at the rate of 3% per annum for 3 years.

Solution

Given, Principal (P) = $500

Rate = 3%

Time (T) = 3 years

Thus Simple Interest (SI) = ?

We know that, SI = PRT

= $500 × 3% × 3

= $5 × 3 × 3 = $45

Thus, Simple Interest (SI) = $45 Answer

Alternate method (Unitary Method) to calculate the Simple Interest (SI)

Given, Principal (P) = $500

Rate = 3%

Time (T) = 3 years

Thus Simple Interest (SI) = ?

Here, rate 3% per annum.

This means $3 will be the interest on $100 for one year.

Now, since on $100 the simple interest for one year = $3

∴ on $1, the simple interest for one year = 3/100

∴ on $500, the simple interest for one year

Thus, on $500 the simple interest for 1 year = $ 15

Therefore, the simple interest for 3 years = $15 × 3 = $45

Thus, simple interest = $45 Answer

Question (3) $300 is borrowed for 5 years. What will the total simple interest at the rate of 8% per annum?

Solution

Given,

Principal (P) = $300

Rate (R) = 8% per annum

Time (T) = 5 years

Thus, Simple Interest (SI) = ?

We know that, Simple Interest (SI) = Principal (P) × Rate (R) × Time (T)

= $300 × 8% × 5

= $15 × 8 = $120

Thus, Simple Interest (SI) = $120 Answer

Alternate method (Unitary Method) to calculate the Simple Interest (SI)

Given,

Principal (P) = $300

Rate (R) = 8% per annum

Time (T) = 5 years

Thus, Simple Interest (SI) = ?

Here, rate 8% per annum.

This means $8 will be the interest on $100 for one year.

Now, since on $100 the simple interest for one year = $8

∴ on $1, the simple interest for one year = 8/100

∴ on $300, the simple interest for one year

Thus, on $300 the simple interest for 1 year = $24

Therefore, the simple interest for 5 years = $24 × 5 = $120

Thus, simple interest = $120 Answer

Question (4) A sum of $1200 is borrowed for 6 months. What will be simple interest to be paid at the rate of 6% per annum?

Solution

Given, Principal (P) = $1200

Rate (R) = 6% per annum

Time (T) = 6 months

Thus, Simple Interest (SI) = ?

Here, time is given in the month, so it is needed to be converted it into years to calculate the interest.

Time (T) = 6 month

= 6/12 year = 1/2 year

Now, we know that, Simple Interest (SI) = P × R × T

= $1200 × 6% × 1/2

= $12 × 3 × 1

= $36

Thus, Simple Interest (SI) = $36 Answer

Alternate method (Unitary Method) to calculate the Simple Interest (SI)

Here given, Principal (P) = $1200

Rate (R) = 6% per annum

Time = 6 months

Thus, Simple Interest (SI) = ?

∵ On $100 the simple interest for one year = $6

∴ On $1, the simple interest for one year = $6/100

∴ ON $1200 the simple interest for one year

= 6 × 12 = $72

Now, the simple interest for one year i.e. 12 months = $72

Thus, the simple interest for 1/2 years, i.e. for 6 months = $72/2 = $36

Thus, Simple Interest = $36 Answer

Question (5) Calculate the simple interest at 9% on a sum of $3000 for 9 months.

Solution

Given,

Principal (P) = $3000

Rate (R) = 9% per annum

Time (T) = 9 month

Thus, Simple Interest (SI) = ?

Here, time is given in month. And rate of interest is per annum, i.e. per year.

Thus, for ease of calculation, time will be converted into years.

Time = 9 months

= 9/12 year = 3/4 year

Now, we know that,

Simple Interest (SI) = Principal (P) × Rate (R) × Time (T)

= 3000 × 9% × 3/4

= $202.50

Thus, simple interest (SI) = $202.50 Answer

Alternate method (Unitary Method) to calculate the Simple Interest (SI)

Given,

Principal (P) = $3000

Rate (R) = 9% per annum

Time (T) = 9 month

Thus, Simple Interest (SI) = ?

Here, time is given in month. And rate of interest is per annum, i.e. per year.

Time = 9 month = 9/12 years

And since rate of interest = 9%

This means, the rate is $9 per $100

Now,

∵ On $100 the simple interest for one year = $9

∴ On $1, the simple interest for one year = $9/100

∴ On $3000 the simple interest for 1 year

= 9 × 30 = $270

∴ $3000 the simple interest for 9/12 years

Thus, the simple interest for 9/12 years, i.e. for 9 months = 810/4 = $202.50

Thus, Simple Interest = $202.50 Answer

Question (6) A sum of $5000 has been borrowed for 3 months. Calculate the simple interest on it at 12% per annum.

Solution

Given,

Principal (P) = $5000

Rate (R) = 12% per annum

Time (T) = 3 month

Thus, Simple Interest (SI) = ?

Here, time is given in month. And rate of interest is per annum, i.e. per year.

Thus, for ease of calculation, time will be converted into years.

Time = 3 months

= 3/12 year = 1/4 year

Now, we know that,

Simple Interest (SI) = Principal (P) × Rate (R) × Time (T)

= 5000 × 12% × 1/4

= 50 × 3 = $150

Thus, simple interest (SI) = $150 Answer

Alternate method (Unitary Method) to calculate the Simple Interest (SI)

Given,

Principal (P) = $5000

Rate (R) = 12% per annum

Time (T) = 3 month

Thus, Simple Interest (SI) = ?

Here, time is given in month. And rate of interest is per annum, i.e. per year.

Thus, for ease of calculation, time will be converted into years.

Time = 3 months

= 3/12 year = 1/4 year

Here, the rate of interest = 12%

This means, the rate of interest is $12 per $100 per year

Thus, rate of interest for 1/4 year on $100 = 12/4 = $3

Now,

∵ On $100 the simple interest for 1/4 year = $3

∴ On $1, the simple interest for 1/4 year = $3/100

∴ On $5000 the simple interest for 1/4 year

= 3 × 50 = $150

Thus, the simple interest for 1/4 years, i.e. for 3 months =$150

Thus, Simple Interest = $150 Answer

Question (7) What will the simple interest at 18% on a sum of $250 borrowed for 2 years 6 months.

Solution

Given,

Principal (P) = $250

Rate (R) = 18% per annum

Time (T) = 2 years 6 months = 2.5 years

Thus, Simple Interest = ?

Here, Rate = 18% = 18/100 = 0.18

Now, we know that, Simple Interest (SI) = Principal (P) × Rate (R) × Time (T)

= $250 × 0.18 × 2.5

= $250 × 0.45

= $112.50

Thus, simple interest = $112.50 Answer

Alternate method (Unitary Method) to calculate the Simple Interest (SI)

Given,

Principal (P) = $250

Rate (R) = 18% per annum

Time (T) = 2 years 6 months = 2.5 years

Thus, Simple Interest = ?

Here, Rate of interest = 18%

This means on $100, the interest per year = $18

Now, since on $100, the interest for 1 year = $18

∴ On $1, the interest for 1 year = 18/100 = 0.18

∴ On $250, the interest for 1 year = 0.18 × 250

&therefore, On $250, the interest for 2.5 years = 0.18 × 250 × 2.5

= $112.50

Thus, simple interest = $112.50 Answer