Simple Interest
MCQs Math


Question:     If Charles paid $4524 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.


Correct Answer  $3900

Solution And Explanation

Solution

Given,

Amount (A) = $4524

Rate of Simple Interest (R) = 4%

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

$4524 = P (1 + 4% × 4)

⇒ $4524 = P (1 + 4/100 × 4)

⇒ $4524 = P (1 + 4 × 4/100)

⇒ $4524 = P (1 + 16/100)

⇒ $4524 = P (100 + 16/100)

⇒ $4524 = P × 116/100

⇒ P × 116/100 = $4524

⇒ P = 4524/116/100

⇒ P = 4524 × 100/116

⇒ P = 4524 × 100/116

⇒ P = 452400/116

⇒ P = $3900

Thus, the sum borrowed (P) = $3900 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 = 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 × 4 = 16

Thus, simple interest for 4 years = 16

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 16 = 116

Calculation of the Principal

Now,

∵ If the Amount is 116, then the Principal = 100

∴ If the Amount is 1, then the Principal = 100/116

∴ If the Amount is 4524, then the Principal = 100/116 × 4524

= 100 × 4524/116

= 452400/116

= 3900

Thus, Principal = $3900

Thus, the sum borrowed = $3900 Answer


Similar Questions

(1) Calculate the amount due if Christopher borrowed a sum of $4000 at 4% simple interest for 4 years.

(2) Calculate the amount due if Mary borrowed a sum of $3050 at 4% simple interest for 4 years.

(3) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $8170 to clear the loan, then find the time period of the loan.

(4) Find the amount to be paid if Karen borrowed a sum of $5950 at 5% simple interest for 8 years.

(5) Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $9280 to clear the loan, then find the time period of the loan.

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

(7) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $11008 to clear the loan, then find the time period of the loan.

(8) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $8476 to clear the loan, then find the time period of the loan.

(9) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $11160 to clear the loan, then find the time period of the loan.

(10) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $9240 to clear the loan, then find the time period of the loan.


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