Simple Interest
MCQs Math


Question:     If Emily paid $5130 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.


Correct Answer  $4750

Solution And Explanation

Solution

Given,

Amount (A) = $5130

Rate of Simple Interest (R) = 2%

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

$5130 = P (1 + 2% × 4)

⇒ $5130 = P (1 + 2/100 × 4)

⇒ $5130 = P (1 + 2 × 4/100)

⇒ $5130 = P (1 + 8/100)

⇒ $5130 = P (100 + 8/100)

⇒ $5130 = P × 108/100

⇒ P × 108/100 = $5130

⇒ P = 5130/108/100

⇒ P = 5130 × 100/108

⇒ P = 5130 × 100/108

⇒ P = 513000/108

⇒ P = $4750

Thus, the sum borrowed (P) = $4750 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 = 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 × 2 = 8

Thus, simple interest for 4 years = 8

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 8 = 108

Calculation of the Principal

Now,

∵ If the Amount is 108, then the Principal = 100

∴ If the Amount is 1, then the Principal = 100/108

∴ If the Amount is 5130, then the Principal = 100/108 × 5130

= 100 × 5130/108

= 513000/108

= 4750

Thus, Principal = $4750

Thus, the sum borrowed = $4750 Answer


Similar Questions

(1) In how much time a principal of $3100 will amount to $3286 at a simple interest of 3% per annum?

(2) Andrew had to pay $5232 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(3) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 4% simple interest?

(4) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $6936 to clear the loan, then find the time period of the loan.

(5) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $9120 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due if Jessica borrowed a sum of $3750 at 4% simple interest for 4 years.

(7) Calculate the amount due if Robert borrowed a sum of $3100 at 10% simple interest for 3 years.

(8) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $7661 to clear the loan, then find the time period of the loan.

(9) If Kimberly paid $5022 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(10) If Christopher borrowed $4000 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.


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