Simple Interest
MCQs Math


Question:     If Daniel paid $4920 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.


Correct Answer  $4100

Solution And Explanation

Solution

Given,

Amount (A) = $4920

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

$4920 = P (1 + 5% × 4)

⇒ $4920 = P (1 + 5/100 × 4)

⇒ $4920 = P (1 + 5 × 4/100)

⇒ $4920 = P (1 + 20/100)

⇒ $4920 = P (100 + 20/100)

⇒ $4920 = P × 120/100

⇒ P × 120/100 = $4920

⇒ P = 4920/120/100

⇒ P = 4920 × 100/120

⇒ P = 4920 × 100/120

⇒ P = 492000/120

⇒ P = $4100

Thus, the sum borrowed (P) = $4100 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 4920, then the Principal = 100/120 × 4920

= 100 × 4920/120

= 492000/120

= 4100

Thus, Principal = $4100

Thus, the sum borrowed = $4100 Answer


Similar Questions

(1) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 8% simple interest?

(2) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $11222 to clear the loan, then find the time period of the loan.

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

(4) Calculate the amount due if Susan borrowed a sum of $3650 at 3% simple interest for 4 years.

(5) If Christopher paid $4640 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(6) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $8740 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due if James borrowed a sum of $3000 at 9% simple interest for 3 years.

(8) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $5984 to clear the loan, then find the time period of the loan.

(9) How much loan did Brian borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7920 to clear it?

(10) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 5% simple interest for 7 years.


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