Simple Interest
MCQs Math


Question:     How much loan did Carol borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7755 to clear it?


Correct Answer  $7050

Solution And Explanation

Solution

Given,

Amount (A) = $7755

Rate of Simple Interest (R) = 2%

Time (T) = 5 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

$7755 = P (1 + 2% × 5)

⇒ $7755 = P (1 + 2/100 × 5)

⇒ $7755 = P (1 + 2 × 5/100)

⇒ $7755 = P (1 + 10/100)

⇒ $7755 = P (100 + 10/100)

⇒ $7755 = P × 110/100

⇒ P × 110/100 = $7755

⇒ P = 7755/110/100

⇒ P = 7755 × 100/110

⇒ P = 7755 × 100/110

⇒ P = 775500/110

⇒ P = $7050

Thus, the sum borrowed (P) = $7050 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 = 2% per annum

Thus, Interest = 2% of principal

⇒ Interest = 2% of 100 = 2

Thus, Simple Interest for 1 year = 2

Calculation of the Amount

Since, in the question, time = 5 years

So, we need to calculate the simple interest for the given time period, which is 5 years

Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year

= 5 × 2 = 10

Thus, simple interest for 5 years = 10

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 10 = 110

Calculation of the Principal

Now,

∵ If the Amount is 110, then the Principal = 100

∴ If the Amount is 1, then the Principal = 100/110

∴ If the Amount is 7755, then the Principal = 100/110 × 7755

= 100 × 7755/110

= 775500/110

= 7050

Thus, Principal = $7050

Thus, the sum borrowed = $7050 Answer


Similar Questions

(1) Find the amount to be paid if Richard borrowed a sum of $5600 at 2% simple interest for 7 years.

(2) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $10164 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 7% simple interest.

(4) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $9702 to clear the loan, then find the time period of the loan.

(5) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $11560 to clear the loan, then find the time period of the loan.

(6) Find the amount to be paid if David borrowed a sum of $5400 at 7% simple interest for 8 years.

(7) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 3% simple interest.

(8) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 2% simple interest for 8 years.

(9) Charles had to pay $4485 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(10) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 10% simple interest.


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