Simple Interest
MCQs Math


Question:     How much loan did Kevin borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8520 to clear it?


Correct Answer  $7100

Solution And Explanation

Solution

Given,

Amount (A) = $8520

Rate of Simple Interest (R) = 4%

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

$8520 = P (1 + 4% × 5)

⇒ $8520 = P (1 + 4/100 × 5)

⇒ $8520 = P (1 + 4 × 5/100)

⇒ $8520 = P (1 + 20/100)

⇒ $8520 = P (100 + 20/100)

⇒ $8520 = P × 120/100

⇒ P × 120/100 = $8520

⇒ P = 8520/120/100

⇒ P = 8520 × 100/120

⇒ P = 8520 × 100/120

⇒ P = 852000/120

⇒ P = $7100

Thus, the sum borrowed (P) = $7100 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 = 4% per annum

Thus, Interest = 4% of principal

⇒ Interest = 4% of 100 = 4

Thus, Simple Interest for 1 year = 4

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 × 4 = 20

Thus, simple interest for 5 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 8520, then the Principal = 100/120 × 8520

= 100 × 8520/120

= 852000/120

= 7100

Thus, Principal = $7100

Thus, the sum borrowed = $7100 Answer


Similar Questions

(1) Find the amount to be paid if John borrowed a sum of $5200 at 5% simple interest for 7 years.

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

(3) Thomas took a loan of $5600 at the rate of 7% simple interest per annum. If he paid an amount of $8344 to clear the loan, then find the time period of the loan.

(4) How much loan did Susan borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6780 to clear it?

(5) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 7% simple interest.

(6) If Lisa paid $4536 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(7) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $7600 to clear the loan, then find the time period of the loan.

(8) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 6% simple interest?

(9) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $8145 to clear the loan, then find the time period of the loan.

(10) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 8% simple interest?


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