Simple Interest
MCQs Math


Question:     How much loan did Deborah borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8940 to clear it?


Correct Answer  $7450

Solution And Explanation

Solution

Given,

Amount (A) = $8940

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

$8940 = P (1 + 4% × 5)

⇒ $8940 = P (1 + 4/100 × 5)

⇒ $8940 = P (1 + 4 × 5/100)

⇒ $8940 = P (1 + 20/100)

⇒ $8940 = P (100 + 20/100)

⇒ $8940 = P × 120/100

⇒ P × 120/100 = $8940

⇒ P = 8940/120/100

⇒ P = 8940 × 100/120

⇒ P = 8940 × 100/120

⇒ P = 894000/120

⇒ P = $7450

Thus, the sum borrowed (P) = $7450 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 8940, then the Principal = 100/120 × 8940

= 100 × 8940/120

= 894000/120

= 7450

Thus, Principal = $7450

Thus, the sum borrowed = $7450 Answer


Similar Questions

(1) Find the amount to be paid if John borrowed a sum of $5200 at 6% simple interest for 8 years.

(2) Calculate the amount due if Barbara borrowed a sum of $3550 at 2% simple interest for 3 years.

(3) If Jennifer paid $3510 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(4) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 9% simple interest?

(5) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $10880 to clear the loan, then find the time period of the loan.

(6) If Joshua paid $5292 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(7) Calculate the amount due if William borrowed a sum of $3500 at 7% simple interest for 3 years.

(8) If Michael borrowed $3300 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(9) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $9768 to clear the loan, then find the time period of the loan.

(10) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $8800 to clear the loan, then find the time period of the loan.


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