Simple Interest
MCQs Math


Question:     How much loan did Emily borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7762.5 to clear it?


Correct Answer  $6750

Solution And Explanation

Solution

Given,

Amount (A) = $7762.5

Rate of Simple Interest (R) = 3%

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

$7762.5 = P (1 + 3% × 5)

⇒ $7762.5 = P (1 + 3/100 × 5)

⇒ $7762.5 = P (1 + 3 × 5/100)

⇒ $7762.5 = P (1 + 15/100)

⇒ $7762.5 = P (100 + 15/100)

⇒ $7762.5 = P × 115/100

⇒ P × 115/100 = $7762.5

⇒ P = 7762.5/115/100

⇒ P = 7762.5 × 100/115

⇒ P = 7762.5 × 100/115

⇒ P = 776250/115

⇒ P = $6750

Thus, the sum borrowed (P) = $6750 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 = 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 × 3 = 15

Thus, simple interest for 5 years = 15

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 15 = 115

Calculation of the Principal

Now,

∵ If the Amount is 115, then the Principal = 100

∴ If the Amount is 1, then the Principal = 100/115

∴ If the Amount is 7762.5, then the Principal = 100/115 × 7762.5

= 100 × 7762.5/115

= 776250/115

= 6750

Thus, Principal = $6750

Thus, the sum borrowed = $6750 Answer


Similar Questions

(1) Calculate the amount due if David borrowed a sum of $3400 at 7% simple interest for 3 years.

(2) In how much time a principal of $3150 will amount to $3339 at a simple interest of 3% per annum?

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

(4) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 7% simple interest.

(5) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 8% simple interest?

(6) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 9% simple interest.

(7) If Susan paid $3942 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(8) Anthony had to pay $4816 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(9) If Donna paid $5626 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(10) David took a loan of $4800 at the rate of 7% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.


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