Simple Interest
Finding sum when time, amount and rate of simple interest are given
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 `=100/160xx960`
= 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 `=100/180xx2160`
= 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 `=100/175xx4375`
= 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 `=100/160xx8000`
= 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 `=100/280xx19600`
= 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 `=100/244xx3782`
= 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 `=100/149.50xx4036.50`
= 100 × 27 = $2700
Thus, the borrowed sum = $2700 Answer
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