Simple Interest
MCQs Math


Question:     If Matthew paid $4704 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.


Correct Answer  $4200

Solution And Explanation

Solution

Given,

Amount (A) = $4704

Rate of Simple Interest (R) = 3%

Time (T) = 4 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

$4704 = P (1 + 3% × 4)

⇒ $4704 = P (1 + 3/100 × 4)

⇒ $4704 = P (1 + 3 × 4/100)

⇒ $4704 = P (1 + 12/100)

⇒ $4704 = P (100 + 12/100)

⇒ $4704 = P × 112/100

⇒ P × 112/100 = $4704

⇒ P = 4704/112/100

⇒ P = 4704 × 100/112

⇒ P = 4704 × 100/112

⇒ P = 470400/112

⇒ P = $4200

Thus, the sum borrowed (P) = $4200 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 = 3% per annum

Thus, Interest = 3% of principal

⇒ Interest = 3% of 100 = 3

Thus, Simple Interest for 1 year = 3

Calculation of the Amount

Since, in the question, time = 4 years

So, we need to calculate the simple interest for the given time period, which is 4 years

Thus, Simple Interest for 4 years = 4 × Simple Interest for 1 year

= 4 × 3 = 12

Thus, simple interest for 4 years = 12

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 12 = 112

Calculation of the Principal

Now,

∵ If the Amount is 112, then the Principal = 100

∴ If the Amount is 1, then the Principal = 100/112

∴ If the Amount is 4704, then the Principal = 100/112 × 4704

= 100 × 4704/112

= 470400/112

= 4200

Thus, Principal = $4200

Thus, the sum borrowed = $4200 Answer


Similar Questions

(1) How much loan did Matthew borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7130 to clear it?

(2) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 5% simple interest.

(3) Calculate the amount due if Jennifer borrowed a sum of $3250 at 9% simple interest for 3 years.

(4) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 9% simple interest?

(5) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 7% simple interest?

(6) How much loan did Linda borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6152.5 to clear it?

(7) In how much time a principal of $3200 will amount to $3392 at a simple interest of 2% per annum?

(8) If Donna paid $5432 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(9) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 4% simple interest.

(10) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $9204 to clear the loan, then find the time period of the loan.


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