Simple Interest
MCQs Math


Question:     How much loan did Edward borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8360 to clear it?


Correct Answer  $7600

Solution And Explanation

Solution

Given,

Amount (A) = $8360

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

$8360 = P (1 + 2% × 5)

⇒ $8360 = P (1 + 2/100 × 5)

⇒ $8360 = P (1 + 2 × 5/100)

⇒ $8360 = P (1 + 10/100)

⇒ $8360 = P (100 + 10/100)

⇒ $8360 = P × 110/100

⇒ P × 110/100 = $8360

⇒ P = 8360/110/100

⇒ P = 8360 × 100/110

⇒ P = 8360 × 100/110

⇒ P = 836000/110

⇒ P = $7600

Thus, the sum borrowed (P) = $7600 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 8360, then the Principal = 100/110 × 8360

= 100 × 8360/110

= 836000/110

= 7600

Thus, Principal = $7600

Thus, the sum borrowed = $7600 Answer


Similar Questions

(1) How much loan did Amanda borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8580 to clear it?

(2) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 3% simple interest.

(3) Calculate the amount due if Thomas borrowed a sum of $3800 at 7% simple interest for 3 years.

(4) Find the amount to be paid if Michael borrowed a sum of $5300 at 3% simple interest for 8 years.

(5) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 2% simple interest for 4 years.

(6) Find the amount to be paid if Patricia borrowed a sum of $5150 at 6% simple interest for 7 years.

(7) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $8313 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 3% simple interest.

(9) If John paid $3840 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(10) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 4% simple interest for 3 years.


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