Simple Interest
MCQs Math


Question:     If James paid $3600 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.


Correct Answer  $3000

Solution And Explanation

Solution

Given,

Amount (A) = $3600

Rate of Simple Interest (R) = 5%

Time (T) = 4 years

Thus, Principal (P) = ?

Method (1) Using Formula

Calculation of the Principal using forumula when Amount, Time and Rate of Simple Interest are given

Formula to find the Principal (P)

Amount (A) = Principal (P) + Principal (P) × Rate (R) × Time (T)

⇒ Amount (A) = Principal (P) [1 + Rate (R) × Time (T)]

⇒ A = P (1 + RT)

Using the formula to find the Amount (A), the fourth can be calculated if any three of A, P, R, and T are given

In the given question, we need to find the Principal (P)

Therefore, by substituting, Amount, Rate, and Time, in the formula A = P (1 + RT) we get

$3600 = P (1 + 5% × 4)

⇒ $3600 = P (1 + 5/100 × 4)

⇒ $3600 = P (1 + 5 × 4/100)

⇒ $3600 = P (1 + 20/100)

⇒ $3600 = P (100 + 20/100)

⇒ $3600 = P × 120/100

⇒ P × 120/100 = $3600

⇒ P = 3600/120/100

⇒ P = 3600 × 100/120

⇒ P = 3600 × 100/120

⇒ P = 360000/120

⇒ P = $3000

Thus, the sum borrowed (P) = $3000 Answer

Method (1) Using Unitary Method

Calculation of the Principal using unitary method when Amount, Time and Rate of Simple Interest are given

Calculation of the Simple Interest

Let, the principal = 100

Here, since rate of simple interest = 5% per annum

Thus, Interest = 5% of principal

⇒ Interest = 5% of 100 = 5

Thus, Simple Interest for 1 year = 5

Calculation of the Amount

Since, in the question, time = 4 years

So, we need to calculate the simple interest for the given time period, which is 4 years

Thus, Simple Interest for 4 years = 4 × Simple Interest for 1 year

= 4 × 5 = 20

Thus, simple interest for 4 years = 20

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 20 = 120

Calculation of the Principal

Now,

∵ If the Amount is 120, then the Principal = 100

∴ If the Amount is 1, then the Principal = 100/120

∴ If the Amount is 3600, then the Principal = 100/120 × 3600

= 100 × 3600/120

= 360000/120

= 3000

Thus, Principal = $3000

Thus, the sum borrowed = $3000 Answer


Similar Questions

(1) Find the amount to be paid if Susan borrowed a sum of $5650 at 10% simple interest for 7 years.

(2) If Emily paid $5510 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(3) Find the amount to be paid if Patricia borrowed a sum of $5150 at 10% simple interest for 8 years.

(4) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 3% simple interest.

(5) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 4% simple interest?

(6) How much loan did David borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6480 to clear it?

(7) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $8732 to clear the loan, then find the time period of the loan.

(8) In how much time a principal of $3200 will amount to $3456 at a simple interest of 2% per annum?

(9) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $10540 to clear the loan, then find the time period of the loan.

(10) If Patricia paid $3528 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.


NCERT Solution and CBSE Notes for class twelve, eleventh, tenth, ninth, seventh, sixth, fifth, fourth and General Math for competitive Exams. ©