Simple Interest
MCQs Math


Question:     How much loan did Robert borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5610 to clear it?


Correct Answer  $5100

Solution And Explanation

Solution

Given,

Amount (A) = $5610

Rate of Simple Interest (R) = 2%

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

$5610 = P (1 + 2% × 5)

⇒ $5610 = P (1 + 2/100 × 5)

⇒ $5610 = P (1 + 2 × 5/100)

⇒ $5610 = P (1 + 10/100)

⇒ $5610 = P (100 + 10/100)

⇒ $5610 = P × 110/100

⇒ P × 110/100 = $5610

⇒ P = 5610/110/100

⇒ P = 5610 × 100/110

⇒ P = 5610 × 100/110

⇒ P = 561000/110

⇒ P = $5100

Thus, the sum borrowed (P) = $5100 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 = 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 × 2 = 10

Thus, simple interest for 5 years = 10

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 10 = 110

Calculation of the Principal

Now,

∵ If the Amount is 110, then the Principal = 100

∴ If the Amount is 1, then the Principal = 100/110

∴ If the Amount is 5610, then the Principal = 100/110 × 5610

= 100 × 5610/110

= 561000/110

= 5100

Thus, Principal = $5100

Thus, the sum borrowed = $5100 Answer


Similar Questions

(1) Calculate the amount due if Michael borrowed a sum of $3300 at 6% simple interest for 4 years.

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

(3) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 5% simple interest.

(4) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 6% simple interest?

(5) In how much time a principal of $3050 will amount to $3507.5 at a simple interest of 3% per annum?

(6) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $9720 to clear the loan, then find the time period of the loan.

(7) If Barbara paid $3976 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(8) If Christopher borrowed $4000 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(9) Calculate the amount due if James borrowed a sum of $3000 at 8% simple interest for 3 years.

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


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