Simple Interest
MCQs Math


Question:     Mark had to pay $4928 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.


Correct Answer  $4400

Solution And Explanation

Solution

Given,

Amount (A) = $4928

Rate of Simple Interest (R) = 4%

Time (T) = 3 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

$4928 = P (1 + 4% × 3)

⇒ $4928 = P (1 + 4/100 × 3)

⇒ $4928 = P (1 + 4 × 3/100)

⇒ $4928 = P (1 + 12/100)

⇒ $4928 = P (100 + 12/100)

⇒ $4928 = P × 112/100

⇒ P × 112/100 = $4928

⇒ P = 4928/112/100

⇒ P = 4928 × 100/112

⇒ P = 4928 × 100/112

⇒ P = 492800/112

⇒ P = $4400

Thus, the sum borrowed (P) = $4400 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 = 3 years

So, we need to calculate the simple interest for the given time period, which is 3 years

Thus, Simple Interest for 3 years = 3 × Simple Interest for 1 year

= 3 × 4 = 12

Thus, simple interest for 3 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 4928, then the Principal = 100/112 × 4928

= 100 × 4928/112

= 492800/112

= 4400

Thus, Principal = $4400

Thus, the sum borrowed = $4400 Answer


Similar Questions

(1) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 4% simple interest?

(2) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $7100 to clear the loan, then find the time period of the loan.

(3) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 2% simple interest?

(4) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 7% simple interest?

(5) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $8840 to clear the loan, then find the time period of the loan.

(6) Find the amount to be paid if Susan borrowed a sum of $5650 at 6% simple interest for 7 years.

(7) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 9% simple interest.

(8) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $8732 to clear the loan, then find the time period of the loan.

(9) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $7360 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due if Susan borrowed a sum of $3650 at 5% simple interest for 4 years.


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