Simple Interest
MCQs Math


Question:     If Mark paid $4928 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.


Correct Answer  $4400

Solution And Explanation

Solution

Given,

Amount (A) = $4928

Rate of Simple Interest (R) = 3%

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

$4928 = P (1 + 3% × 4)

⇒ $4928 = P (1 + 3/100 × 4)

⇒ $4928 = P (1 + 3 × 4/100)

⇒ $4928 = P (1 + 12/100)

⇒ $4928 = P (100 + 12/100)

⇒ $4928 = P × 112/100

⇒ P × 112/100 = $4928

⇒ P = 4928/112/100

⇒ P = 4928 × 100/112

⇒ P = 4928 × 100/112

⇒ P = 492800/112

⇒ P = $4400

Thus, the sum borrowed (P) = $4400 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 = 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 × 3 = 12

Thus, simple interest for 4 years = 12

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 12 = 112

Calculation of the Principal

Now,

∵ If the Amount is 112, then the Principal = 100

∴ If the Amount is 1, then the Principal = 100/112

∴ If the Amount is 4928, then the Principal = 100/112 × 4928

= 100 × 4928/112

= 492800/112

= 4400

Thus, Principal = $4400

Thus, the sum borrowed = $4400 Answer


Similar Questions

(1) Calculate the amount due if Patricia borrowed a sum of $3150 at 7% simple interest for 4 years.

(2) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 2% simple interest?

(3) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 9% simple interest?

(4) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $10212 to clear the loan, then find the time period of the loan.

(5) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $9685 to clear the loan, then find the time period of the loan.

(6) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 3% simple interest?

(7) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $11730 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due if Joseph borrowed a sum of $3700 at 2% simple interest for 4 years.

(9) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $10595 to clear the loan, then find the time period of the loan.

(10) If Kenneth paid $5800 to settle his loan which he had taken 4 years before at a simple interest of 4%, 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. ©