Simple Interest
MCQs Math


Question:     If Betty paid $4930 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.


Correct Answer  $4250

Solution And Explanation

Solution

Given,

Amount (A) = $4930

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

$4930 = P (1 + 4% × 4)

⇒ $4930 = P (1 + 4/100 × 4)

⇒ $4930 = P (1 + 4 × 4/100)

⇒ $4930 = P (1 + 16/100)

⇒ $4930 = P (100 + 16/100)

⇒ $4930 = P × 116/100

⇒ P × 116/100 = $4930

⇒ P = 4930/116/100

⇒ P = 4930 × 100/116

⇒ P = 4930 × 100/116

⇒ P = 493000/116

⇒ P = $4250

Thus, the sum borrowed (P) = $4250 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 4930, then the Principal = 100/116 × 4930

= 100 × 4930/116

= 493000/116

= 4250

Thus, Principal = $4250

Thus, the sum borrowed = $4250 Answer


Similar Questions

(1) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 5% simple interest.

(2) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $7680 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 8% simple interest for 3 years.

(4) How much loan did Karen borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6545 to clear it?

(5) How much loan did Joseph borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7125 to clear it?

(6) If Kenneth paid $5800 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(7) How much loan did Patricia borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5665 to clear it?

(8) Calculate the amount due if David borrowed a sum of $3400 at 6% simple interest for 4 years.

(9) Calculate the amount due if Thomas borrowed a sum of $3800 at 8% simple interest for 4 years.

(10) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $10260 to clear the loan, then find the time period of the loan.


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