Simple Interest
MCQs Math


Question:     Christopher had to pay $4240 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  $4000

Solution And Explanation

Solution

Given,

Amount (A) = $4240

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

$4240 = P (1 + 2% × 3)

⇒ $4240 = P (1 + 2/100 × 3)

⇒ $4240 = P (1 + 2 × 3/100)

⇒ $4240 = P (1 + 6/100)

⇒ $4240 = P (100 + 6/100)

⇒ $4240 = P × 106/100

⇒ P × 106/100 = $4240

⇒ P = 4240/106/100

⇒ P = 4240 × 100/106

⇒ P = 4240 × 100/106

⇒ P = 424000/106

⇒ P = $4000

Thus, the sum borrowed (P) = $4000 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 4240, then the Principal = 100/106 × 4240

= 100 × 4240/106

= 424000/106

= 4000

Thus, Principal = $4000

Thus, the sum borrowed = $4000 Answer


Similar Questions

(1) Find the amount to be paid if James borrowed a sum of $5000 at 7% simple interest for 7 years.

(2) Find the amount to be paid if Richard borrowed a sum of $5600 at 2% simple interest for 7 years.

(3) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 3% simple interest.

(4) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $6664 to clear the loan, then find the time period of the loan.

(5) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.

(6) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 9% simple interest?

(7) How much loan did Daniel borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6710 to clear it?

(8) Calculate the amount due if Karen borrowed a sum of $3950 at 8% simple interest for 4 years.

(9) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 10% 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.


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