Simple Interest
MCQs Math


Question:     How much loan did Jennifer borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6562.5 to clear it?


Correct Answer  $5250

Solution And Explanation

Solution

Given,

Amount (A) = $6562.5

Rate of Simple Interest (R) = 5%

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

$6562.5 = P (1 + 5% × 5)

⇒ $6562.5 = P (1 + 5/100 × 5)

⇒ $6562.5 = P (1 + 5 × 5/100)

⇒ $6562.5 = P (1 + 25/100)

⇒ $6562.5 = P (100 + 25/100)

⇒ $6562.5 = P × 125/100

⇒ P × 125/100 = $6562.5

⇒ P = 6562.5/125/100

⇒ P = 6562.5 × 100/125

⇒ P = 6562.5 × 100/125

⇒ P = 656250/125

⇒ P = $5250

Thus, the sum borrowed (P) = $5250 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 = 5% per annum

Thus, Interest = 5% of principal

⇒ Interest = 5% of 100 = 5

Thus, Simple Interest for 1 year = 5

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 × 5 = 25

Thus, simple interest for 5 years = 25

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 25 = 125

Calculation of the Principal

Now,

∵ If the Amount is 125, then the Principal = 100

∴ If the Amount is 1, then the Principal = 100/125

∴ If the Amount is 6562.5, then the Principal = 100/125 × 6562.5

= 100 × 6562.5/125

= 656250/125

= 5250

Thus, Principal = $5250

Thus, the sum borrowed = $5250 Answer


Similar Questions

(1) Calculate the amount due if Robert borrowed a sum of $3100 at 4% simple interest for 4 years.

(2) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $11730 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due if Thomas borrowed a sum of $3800 at 6% simple interest for 4 years.

(4) If Charles paid $4368 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(5) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 3% simple interest.

(6) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $7172 to clear the loan, then find the time period of the loan.

(7) How much loan did Richard borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6440 to clear it?

(8) If Daniel paid $4428 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(9) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 5% simple interest.

(10) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 9% simple interest.


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