Simple Interest
MCQs Math


Question:     If William paid $3920 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.


Correct Answer  $3500

Solution And Explanation

Solution

Given,

Amount (A) = $3920

Rate of Simple Interest (R) = 3%

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

$3920 = P (1 + 3% × 4)

⇒ $3920 = P (1 + 3/100 × 4)

⇒ $3920 = P (1 + 3 × 4/100)

⇒ $3920 = P (1 + 12/100)

⇒ $3920 = P (100 + 12/100)

⇒ $3920 = P × 112/100

⇒ P × 112/100 = $3920

⇒ P = 3920/112/100

⇒ P = 3920 × 100/112

⇒ P = 3920 × 100/112

⇒ P = 392000/112

⇒ P = $3500

Thus, the sum borrowed (P) = $3500 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 = 3% per annum

Thus, Interest = 3% of principal

⇒ Interest = 3% of 100 = 3

Thus, Simple Interest for 1 year = 3

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 × 3 = 12

Thus, simple interest for 4 years = 12

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 12 = 112

Calculation of the Principal

Now,

∵ If the Amount is 112, then the Principal = 100

∴ If the Amount is 1, then the Principal = 100/112

∴ If the Amount is 3920, then the Principal = 100/112 × 3920

= 100 × 3920/112

= 392000/112

= 3500

Thus, Principal = $3500

Thus, the sum borrowed = $3500 Answer


Similar Questions

(1) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 4% simple interest?

(2) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 8% simple interest?

(3) If William paid $3920 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(4) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 10% simple interest?

(5) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 4% simple interest.

(6) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 5% simple interest?

(7) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $8662 to clear the loan, then find the time period of the loan.

(8) Charles took a loan of $5800 at the rate of 8% simple interest per annum. If he paid an amount of $9048 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 3% simple interest.

(10) Find the amount to be paid if John borrowed a sum of $5200 at 7% simple interest for 8 years.


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