Simple Interest
MCQs Math


Question:     Thomas had to pay $4256 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  $3800

Solution And Explanation

Solution

Given,

Amount (A) = $4256

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

$4256 = P (1 + 4% × 3)

⇒ $4256 = P (1 + 4/100 × 3)

⇒ $4256 = P (1 + 4 × 3/100)

⇒ $4256 = P (1 + 12/100)

⇒ $4256 = P (100 + 12/100)

⇒ $4256 = P × 112/100

⇒ P × 112/100 = $4256

⇒ P = 4256/112/100

⇒ P = 4256 × 100/112

⇒ P = 4256 × 100/112

⇒ P = 425600/112

⇒ P = $3800

Thus, the sum borrowed (P) = $3800 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 4256, then the Principal = 100/112 × 4256

= 100 × 4256/112

= 425600/112

= 3800

Thus, Principal = $3800

Thus, the sum borrowed = $3800 Answer


Similar Questions

(1) How much loan did Christopher borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7500 to clear it?

(2) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $7380 to clear the loan, then find the time period of the loan.

(3) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $9600 to clear the loan, then find the time period of the loan.

(4) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.

(5) How much loan did Kimberly borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7315 to clear it?

(6) Calculate the amount due if John borrowed a sum of $3200 at 4% simple interest for 3 years.

(7) How much loan did Laura borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8635 to clear it?

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

(9) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 10% simple interest?

(10) Calculate the amount due if Richard borrowed a sum of $3600 at 7% simple interest for 3 years.


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