Simple Interest
MCQs Math


Question:     If Barbara paid $4260 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.


Correct Answer  $3550

Solution And Explanation

Solution

Given,

Amount (A) = $4260

Rate of Simple Interest (R) = 5%

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

$4260 = P (1 + 5% × 4)

⇒ $4260 = P (1 + 5/100 × 4)

⇒ $4260 = P (1 + 5 × 4/100)

⇒ $4260 = P (1 + 20/100)

⇒ $4260 = P (100 + 20/100)

⇒ $4260 = P × 120/100

⇒ P × 120/100 = $4260

⇒ P = 4260/120/100

⇒ P = 4260 × 100/120

⇒ P = 4260 × 100/120

⇒ P = 426000/120

⇒ P = $3550

Thus, the sum borrowed (P) = $3550 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 = 5% per annum

Thus, Interest = 5% of principal

⇒ Interest = 5% of 100 = 5

Thus, Simple Interest for 1 year = 5

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 × 5 = 20

Thus, simple interest for 4 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 4260, then the Principal = 100/120 × 4260

= 100 × 4260/120

= 426000/120

= 3550

Thus, Principal = $3550

Thus, the sum borrowed = $3550 Answer


Similar Questions

(1) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 6% simple interest.

(2) Calculate the amount due if Robert borrowed a sum of $3100 at 8% simple interest for 4 years.

(3) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 4% simple interest?

(4) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $13110 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 3% simple interest.

(6) Calculate the amount due if Charles borrowed a sum of $3900 at 10% simple interest for 3 years.

(7) Anthony had to pay $4558 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(8) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $11970 to clear the loan, then find the time period of the loan.

(9) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $8460 to clear the loan, then find the time period of the loan.

(10) Find the amount to be paid if James borrowed a sum of $5000 at 8% simple interest for 7 years.


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