Simple Interest - Arithmetic

Question (1) If a sum amounts to $960 in 4 years at simple interest at 15%, then find the sum?

Solution

Given, Amount (A) = $960

Rate (R) = 15%

Time (T) = 4 years

Then, sum or principal = ?

Let Principal or Sum = P

We know that, Amount (A) = P + SI

⇒ A = P + (PRT)

[Because, SI = PRT]

⇒ A = P (1 + RT)

After cross multiplilcation

⇒ P = $600

Thus, principal = $600 Answer

Alternate method to find the sum when amount, rate of simple interest and time has been given

Given, Amount (A) = $960

Rate (R) = 15%

Time (T) = 4 years

Then, sum or principal = ?

Let the principal = P

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

= P × 15% × 4

Now, we know that, Amount (A) = Principal (P) + Simple Interest (SI)

After cross multiplilcation

⇒ P = $600

Thus, principal = $600 Answer

Alternate method (Unitary Method) to find the sum when amount, rate of simple interest and time has been given

Given, Amount (A) = $960

Rate (R) = 15%

Time (T) = 4 years

Then, sum or principal = ?

Let principal = $100

Thus, SI on $100 for 1 year = $15

Therefore, SI on $100 for 4 years = $15 × 4 = $60

⇒ Simple Interest = $60

Therefore, Amount (A) = Principal (P) + Simple Interest (SI)

⇒ A = $100 + $60

⇒ A = $160

Now, when amount is $160, then principal = $100

&therefore, when amount is 1, then principal = $100/$160

&therefore, when amount is $960, then principal

= 100 × 6 = 600

Thus, principal = $600 Answer

Question (2) If a sum amounts to $2160 in 4 years at simple interest at 20%, then find the sum?

Solution

Given, Amount (A) = $2160

Rate (R) = 20%

Time (T) = 4 years

Then, sum or principal = ?

Let Principal or Sum = P

We know that, Amount (A) = P + SI

⇒ A = P + (PRT)

[Because, SI = PRT]

⇒ A = P (1 + RT)

After cross multiplilcation

⇒ P = $240 × 5

⇒ P = $1200

Thus, principal = $1200 Answer

Alternate method to find the sum when amount, rate of simple interest and time has been given

Given, Amount (A) = $2160

Rate (R) = 20%

Time (T) = 4 years

Then, sum or principal = ?

Let the principal = P

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

= P × 20% × 4

Now, we know that, Amount (A) = Principal (P) + Simple Interest (SI)

After cross multiplication

⇒ P = $240 × 5

⇒ P = $1200

Thus, principal = $1200 Answer

Alternate method (Unitary Method) to find the sum when amount, rate of simple interest and time has been given

Given, Amount (A) = $2160

Rate (R) = 20%

Time (T) = 4 years

Then, sum or principal = ?

Let principal = $100

Thus, SI on $100 for 1 year = $20

Therefore, SI on $100 for 4 years = $20 × 4 = $80

⇒ Simple Interest = $80

Therefore, Amount (A) = Principal (P) + Simple Interest (SI)

⇒ A = $100 + $80

⇒ A = $180

Now, when amount is $180, then principal = $100

&therefore, when amount is 1, then principal = $100/$180

&therefore, when amount is $2160, then principal

= 100 × 120 = 1200

Thus, principal = $1200 Answer

Question (3) A person borrowed a sum for at 25% simple interest. If he paid a total amount of $4375 after 3 (three) years to clear the loan, then find the sum borrowed by him?

Solution

Given, Amount (A) = $4375

Rate (R) = 25%

= 25/100 = 0.25

[ Here 25% has been converted to decimal]

Time (T) = 3 years

Thus, the borrowed sum (principal) = ?

Let Principal or Sum = P

We know that, Amount (A) = P + SI

⇒ A = P + (PRT)

[Because, SI = PRT]

⇒ A = P (1 + RT)

⇒ 4375 = P { 1 + (0.25 × 3)}

⇒ $4375 = P { 1 + 0.75 }

⇒ $4375 = P × 1.75

⇒ 1.75 P = $4375

⇒ P = $4375/1.75

⇒ P = $2500

Thus, the borrowed sum = $2500 Answer

Alternate method to find the sum when amount, rate of simple interest and time has been given

Given, Amount (A) = $4375

Rate (R) = 25%

= 25/100 = 0.25

[ Here 25% has been converted to decimal]

Time (T) = 3 years

Thus, the borrowed sum (principal) = ?

Let the principal = P

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

= P × 0.25 × 3

= P × 0.75

⇒ Simple Interest (SI) = 0.75 P

Now, we know that, Amount (A) = Principal (P) + Simple Interest (SI)

⇒ $4375 = P + 0.75 P

⇒ $4375 = P (1 + 0.75 )

⇒ $4375 = P × 1.75

⇒ $4375 = 1.75 P

⇒ 1.75 P = $4375

⇒ P = $4375/1.75

⇒ P = $2500

Thus, the borrowed sum = $2500 Answer

Alternate method (Unitary Method) to find the sum when amount, rate of simple interest and time has been given

Given, Amount (A) = $4375

Rate (R) = 25%

Time (T) = 3 years

Thus, the borrowed sum (principal) = ?

Let principal = $100

Thus, SI on $100 for 1 year = $25

Therefore, SI on $100 for 3 years = $25 × 3 = $75

⇒ Simple Interest = $75

Therefore, Amount (A) = Principal (P) + Simple Interest (SI)

⇒ A = $100 + $75

⇒ A = $175

Now, when amount is $175, then principal = $100

&therefore, when amount is 1, then principal = $100/$175

&therefore, when amount is $4375, then principal

= 100 × 25 = 2500

Thus, the borrowed sum = $2500 Answer

Question (4) A person borrowed a sum for at 12% simple interest for 5 (five) years. If he paid a total amount of $8000 to clear the loan, then find the sum borrowed by him?

Solution

Given, Amount (A) = $8000

Rate (R) = 12%

= 12/100 = 0.12

[ Here 12% has been converted to decimal]

Time (T) = 5 years

Thus, the borrowed sum (principal) = ?

Let Principal or Sum = P

We know that, Amount (A) = P + SI

⇒ A = P + (PRT)

[Because, SI = PRT]

⇒ A = P (1 + RT)

⇒ $8000 = P { 1 + (0.12 × 5)}

⇒ $8000 = P { 1 + 0.6 }

⇒ $8000 = P × 1.6

⇒ 1.6 P = $8000

⇒ P = $8000/1.6

⇒ P = $5000

Thus, the borrowed sum = $5000 Answer

Alternate method to find the sum when amount, rate of simple interest and time has been given

Given, Amount (A) = $8000

Rate (R) = 12%

= 12/100 = 0.12

[ Here 12% has been converted to decimal]

Time (T) = 5 years

Thus, the borrowed sum (principal) = ?

Let the principal = P

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

= P × 0.12 × 5

= P × 0.6

⇒ Simple Interest (SI) = 0.6 P

Now, we know that, Amount (A) = Principal (P) + Simple Interest (SI)

⇒ $8000 = P + 0.6 P

⇒ $8000 = P (1 + 0.6 )

⇒ $8000 = P × 1.6

⇒ $8000 = 1.6 P

⇒ 1.6 P = $8000

⇒ P = $8000/1.6

⇒ P = $5000

Thus, the borrowed sum = $5000 Answer

Alternate method (Unitary Method) to find the sum when amount, rate of simple interest and time has been given

Given, Amount (A) = $8000

Rate (R) = 12%

Time (T) = 5 years

Thus, the borrowed sum (principal) = ?

Let principal = $100

Thus, SI on $100 for 1 year = $12

Therefore, SI on $100 for 5 years = $12 × 6 = $60

⇒ Simple Interest = $60

Therefore, Amount (A) = Principal (P) + Simple Interest (SI)

⇒ A = $100 + $60

⇒ A = $160

Now, when amount is $160, then principal = $100

&therefore, when amount is 1, then principal = $100/$160

&therefore, when amount is $8000, then principal

= 100 × 50 = 5000

Thus, the borrowed sum = $5000 Answer

Question (5) A person borrowed a sum for at 15% simple interest for 12 (twelve) years. If he paid a total amount of $19600 to clear the loan, then find the sum borrowed by him?

Solution

Given, Amount (A) = $19600

Rate (R) = 15%

= 15/100 = 0.15

[ Here 15% has been converted to decimal which is equal to 0.15]

Time (T) = 12 years

Thus, the borrowed sum (principal) = ?

Let Principal or Sum = P

We know that, Amount (A) = P + SI

⇒ A = P + (PRT)

[Because, SI = PRT]

⇒ A = P (1 + RT)

⇒ $19600 = P { 1 + (0.15 × 12)}

⇒ $19600 = P { 1 + 1.8 }

⇒ $19600 = P × 2.8

⇒ 2.8 P = $19600

⇒ P = $19600/2.8

⇒ P = $7000

Thus, the borrowed sum = $7000 Answer

Alternate method to find the sum when amount, rate of simple interest and time has been given

Given, Amount (A) = $19600

Rate (R) = 15%

= 15/100 = 0.15

[ Here 15% has been converted to decimal which is equal to 0.15]

Time (T) = 12 years

Thus, the borrowed sum (principal) = ?

Let the principal = P

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

= P × 0.15 × 12

= P × 1.8

⇒ Simple Interest (SI) = 1.8 P

Now, we know that, Amount (A) = Principal (P) + Simple Interest (SI)

⇒ $19600 = P + 1.8 P

⇒ $19600 = P (1 + 1.8 )

⇒ $19600 = P × 2.8

⇒ $19600 = 2.8 P

⇒ 2.8 P = $19600

⇒ P = $19600/2.8

⇒ P = $7000

Thus, the borrowed sum = $7000 Answer

Alternate method (Unitary Method) to find the sum when amount, rate of simple interest and time has been given

Given, Amount (A) = $19600

Rate (R) = 15%

Time (T) = 12 years

Thus, the borrowed sum (principal) = ?

Let principal = $100

Thus, SI on $100 for 1 year = $15

Therefore, SI on $100 for 12 years = $15 × 12 = $180

⇒ Simple Interest = $180

Therefore, Amount (A) = Principal (P) + Simple Interest (SI)

⇒ A = $100 + $180

⇒ A = $280

Now, when amount is $280, then principal = $100

&therefore, when amount is 1, then principal = $100/$280

&therefore, when amount is $19600, then principal

= 100 × 70 = $7000

Thus, the borrowed sum = $7000 Answer

Question (6) If a person has to pay $3782 to clear his loan, then what sum did he borrow at 16% for 9 years?

Solution

Given, Amount (A) = $3782

Rate (R) = 16%

= 16/100 = 0.16

[ Here for ease of calculation, 16% has been converted to decimal which is equal to 0.16]

Time (T) = 9 years

Thus, the borrowed sum (principal) = ?

Let Principal or Sum = P

We know that, Amount (A) = P + SI

⇒ A = P + (PRT)

[Because, SI = PRT]

⇒ A = P (1 + RT)

⇒ $3782 = P { 1 + (0.16 × 9)}

⇒ $3782 = P { 1 + 1.44 }

⇒ $3782 = P × 2.44

⇒ 2.44 P = $3782

⇒ P = $3782/2.44

⇒ P = $1550

Thus, the borrowed sum = $1550 Answer

Alternate method to find the sum when amount, rate of simple interest and time has been given

Given, Amount (A) = $3782

Rate (R) = 16%

= 16/100 = 0.16

[ Here for ease of calculation, 16% has been converted to decimal which is equal to 0.16]

Time (T) = 9 years

Thus, the borrowed sum (principal) = ?

Let the principal = P

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

= P × 0.16 × 9

= P × 1.44

⇒ Simple Interest (SI) = 1.44 P

Now, we know that, Amount (A) = Principal (P) + Simple Interest (SI)

⇒ $3782 = P + 1.44 P

⇒ $3782 = P (1 + 1.44 )

⇒ $3782 = P × 2.44

⇒ $3782 = 2.44 P

⇒ 2.44 P = $3782

⇒ P = $3782/2.44

⇒ P = $1550

Thus, the borrowed sum = $1550 Answer

Alternate method (Unitary Method) to find the sum when amount, rate of simple interest and time has been given

Given, Amount (A) = $3782

Rate (R) = 16%

Time (T) = 9 years

Thus, the borrowed sum (principal) = ?

Let principal = $100

Thus, SI on $100 for 1 year = $16

Therefore, SI on $100 for 1 years = $16 × 9 = $144

⇒ Simple Interest = $144

Therefore, Amount (A) = Principal (P) + Simple Interest (SI)

⇒ A = $100 + $144

⇒ A = $244

Now, when amount is $244, then principal = $100

&therefore, when amount is 1, then principal = $100/$244

&therefore, when amount is $3782, then principal

= 100 × 15.5 = $1550

Thus, the borrowed sum = $1550 Answer

Question (7) A person borrowed a sum and he has to pay an amount of $4036.50 to clear the loan after two years 9 months. If he borrowed the sum at 18%, then find the sum.

Solution

Given, Amount (A) = $4036.50

Rate (R) = 18%

= 18/100 = 0.18

[ Here for ease of calculation, 18% has been converted to decimal which is equal to 0.18]

Time (T) = 2 years 9 months

= 2 + 9/12 years

= 2 + 0.75 years = 2.75 years

⇒ Time = 2.75 years

Thus, the borrowed sum (principal) = ?

Let Principal or Sum = P

We know that, Amount (A) = P + SI

⇒ A = P + (PRT)

[Because, SI = PRT]

⇒ A = P (1 + RT)

⇒ $4036.50 = P { 1 + (0.18 × 2.75)}

⇒ $4036.50 = P { 1 + 0.495 }

⇒ $4036.50 = P × 1.495

⇒ 1.495 P = $4036.50

⇒ P = $4036.50/1.495

⇒ P = $2700

Thus, the borrowed sum = $2700 Answer

Alternate method to find the sum when amount, rate of simple interest and time has been given

Given, Amount (A) = $4036.50

Rate (R) = 18%

= 18/100 = 0.18

[ Here for ease of calculation, 18% has been converted to decimal which is equal to 0.18]

Time (T) = 2.75 years

Thus, the borrowed sum (principal) = ?

Let the principal = P

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

= P × 0.18 × 2.75

= P × 0.495

⇒ Simple Interest (SI) = 0.495 P

Now, we know that, Amount (A) = Principal (P) + Simple Interest (SI)

⇒ $4036.50 = 1 + 0.495 P

⇒ $4036.50 = P (1 + 0.495 )

⇒ $4036.50 = P × 1.495

⇒ $4036.50 = 1.495 P

⇒ 1.495 P = $4036.50

⇒ P = $4036.50/1.495

⇒ P = $2700

Thus, the borrowed sum = $2700 Answer

Alternate method (Unitary Method) to find the sum when amount, rate of simple interest and time has been given

Given, Amount (A) = $4036.50

Rate (R) = 18%

Time (T) = 2.75 years

Thus, the borrowed sum (principal) = ?

Let principal = $100

Thus, SI on $100 for 1 year = $18

Therefore, SI on $100 for 1 years = $18 × 2.75 = $49.50

⇒ Simple Interest = $49.50

Therefore, Amount (A) = Principal (P) + Simple Interest (SI)

⇒ A = $100 + $49.50

⇒ A = $149.50

Now, when amount is $149.50, then principal = $100

&therefore, when amount is 1, then principal = $100/$149.50

&therefore, when amount is $4036.50, then principal

= 100 × 27 = $2700

Thus, the borrowed sum = $2700 Answer