Simple Interest
MCQs Math


Question:     How much loan did Lisa borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7562.5 to clear it?


Correct Answer  $6050

Solution And Explanation

Solution

Given,

Amount (A) = $7562.5

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

$7562.5 = P (1 + 5% × 5)

⇒ $7562.5 = P (1 + 5/100 × 5)

⇒ $7562.5 = P (1 + 5 × 5/100)

⇒ $7562.5 = P (1 + 25/100)

⇒ $7562.5 = P (100 + 25/100)

⇒ $7562.5 = P × 125/100

⇒ P × 125/100 = $7562.5

⇒ P = 7562.5/125/100

⇒ P = 7562.5 × 100/125

⇒ P = 7562.5 × 100/125

⇒ P = 756250/125

⇒ P = $6050

Thus, the sum borrowed (P) = $6050 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 7562.5, then the Principal = 100/125 × 7562.5

= 100 × 7562.5/125

= 756250/125

= 6050

Thus, Principal = $6050

Thus, the sum borrowed = $6050 Answer


Similar Questions

(1) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $7783 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due if James borrowed a sum of $3000 at 8% simple interest for 4 years.

(3) Find the amount to be paid if John borrowed a sum of $5200 at 10% simple interest for 8 years.

(4) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $8036 to clear the loan, then find the time period of the loan.

(5) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $9231 to clear the loan, then find the time period of the loan.

(6) How much loan did Joshua borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7935 to clear it?

(7) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $13600 to clear the loan, then find the time period of the loan.

(8) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 6% simple interest?

(9) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 6% simple interest.

(10) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 7% simple interest.


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