Simple Interest
MCQs Math


Question:     Joseph had to pay $3922 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.


Correct Answer  $3700

Solution And Explanation

Solution

Given,

Amount (A) = $3922

Rate of Simple Interest (R) = 2%

Time (T) = 3 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

$3922 = P (1 + 2% × 3)

⇒ $3922 = P (1 + 2/100 × 3)

⇒ $3922 = P (1 + 2 × 3/100)

⇒ $3922 = P (1 + 6/100)

⇒ $3922 = P (100 + 6/100)

⇒ $3922 = P × 106/100

⇒ P × 106/100 = $3922

⇒ P = 3922/106/100

⇒ P = 3922 × 100/106

⇒ P = 3922 × 100/106

⇒ P = 392200/106

⇒ P = $3700

Thus, the sum borrowed (P) = $3700 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 = 2% per annum

Thus, Interest = 2% of principal

⇒ Interest = 2% of 100 = 2

Thus, Simple Interest for 1 year = 2

Calculation of the Amount

Since, in the question, time = 3 years

So, we need to calculate the simple interest for the given time period, which is 3 years

Thus, Simple Interest for 3 years = 3 × Simple Interest for 1 year

= 3 × 2 = 6

Thus, simple interest for 3 years = 6

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 6 = 106

Calculation of the Principal

Now,

∵ If the Amount is 106, then the Principal = 100

∴ If the Amount is 1, then the Principal = 100/106

∴ If the Amount is 3922, then the Principal = 100/106 × 3922

= 100 × 3922/106

= 392200/106

= 3700

Thus, Principal = $3700

Thus, the sum borrowed = $3700 Answer


Similar Questions

(1) If Kenneth paid $5600 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(2) How much loan did Paul borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8375 to clear it?

(3) Charles took a loan of $5800 at the rate of 8% simple interest per annum. If he paid an amount of $9512 to clear the loan, then find the time period of the loan.

(4) Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $10824 to clear the loan, then find the time period of the loan.

(5) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $8424 to clear the loan, then find the time period of the loan.

(6) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 9% simple interest?

(7) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $7616 to clear the loan, then find the time period of the loan.

(8) Find the amount to be paid if Robert borrowed a sum of $5100 at 4% simple interest for 7 years.

(9) Find the amount to be paid if Sarah borrowed a sum of $5850 at 10% simple interest for 8 years.

(10) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $7824 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. ©