Simple Interest
MCQs Math


Question:     How much loan did James borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5750 to clear it?


Correct Answer  $5000

Solution And Explanation

Solution

Given,

Amount (A) = $5750

Rate of Simple Interest (R) = 3%

Time (T) = 5 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

$5750 = P (1 + 3% × 5)

⇒ $5750 = P (1 + 3/100 × 5)

⇒ $5750 = P (1 + 3 × 5/100)

⇒ $5750 = P (1 + 15/100)

⇒ $5750 = P (100 + 15/100)

⇒ $5750 = P × 115/100

⇒ P × 115/100 = $5750

⇒ P = 5750/115/100

⇒ P = 5750 × 100/115

⇒ P = 5750 × 100/115

⇒ P = 575000/115

⇒ P = $5000

Thus, the sum borrowed (P) = $5000 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 = 3% per annum

Thus, Interest = 3% of principal

⇒ Interest = 3% of 100 = 3

Thus, Simple Interest for 1 year = 3

Calculation of the Amount

Since, in the question, time = 5 years

So, we need to calculate the simple interest for the given time period, which is 5 years

Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year

= 5 × 3 = 15

Thus, simple interest for 5 years = 15

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 15 = 115

Calculation of the Principal

Now,

∵ If the Amount is 115, then the Principal = 100

∴ If the Amount is 1, then the Principal = 100/115

∴ If the Amount is 5750, then the Principal = 100/115 × 5750

= 100 × 5750/115

= 575000/115

= 5000

Thus, Principal = $5000

Thus, the sum borrowed = $5000 Answer


Similar Questions

(1) Find the amount to be paid if Mary borrowed a sum of $5050 at 3% simple interest for 7 years.

(2) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $9050 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due if Linda borrowed a sum of $3350 at 10% simple interest for 4 years.

(4) If Robert borrowed $3100 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(5) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $11780 to clear the loan, then find the time period of the loan.

(6) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 10% simple interest?

(7) Find the amount to be paid if William borrowed a sum of $5500 at 9% simple interest for 7 years.

(8) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $9860 to clear the loan, then find the time period of the loan.

(9) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 3% simple interest?

(10) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $10320 to clear the loan, then find the time period of the loan.


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