Simple Interest
MCQs Math


Question:     How much loan did Rebecca borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9180 to clear it?


Correct Answer  $7650

Solution And Explanation

Solution

Given,

Amount (A) = $9180

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

$9180 = P (1 + 4% × 5)

⇒ $9180 = P (1 + 4/100 × 5)

⇒ $9180 = P (1 + 4 × 5/100)

⇒ $9180 = P (1 + 20/100)

⇒ $9180 = P (100 + 20/100)

⇒ $9180 = P × 120/100

⇒ P × 120/100 = $9180

⇒ P = 9180/120/100

⇒ P = 9180 × 100/120

⇒ P = 9180 × 100/120

⇒ P = 918000/120

⇒ P = $7650

Thus, the sum borrowed (P) = $7650 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 9180, then the Principal = 100/120 × 9180

= 100 × 9180/120

= 918000/120

= 7650

Thus, Principal = $7650

Thus, the sum borrowed = $7650 Answer


Similar Questions

(1) Calculate the amount due if William borrowed a sum of $3500 at 5% simple interest for 4 years.

(2) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $8930 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due if Charles borrowed a sum of $3900 at 6% simple interest for 3 years.

(4) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 9% simple interest.

(5) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 7% simple interest.

(6) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $9231 to clear the loan, then find the time period of the loan.

(7) How much loan did Linda borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5885 to clear it?

(8) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 2% simple interest?

(9) If Donald paid $5040 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(10) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $9000 to clear the loan, then find the time period of the loan.


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