Simple Interest
MCQs Math


Question:     How much loan did Sharon borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8912.5 to clear it?


Correct Answer  $7750

Solution And Explanation

Solution

Given,

Amount (A) = $8912.5

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

$8912.5 = P (1 + 3% × 5)

⇒ $8912.5 = P (1 + 3/100 × 5)

⇒ $8912.5 = P (1 + 3 × 5/100)

⇒ $8912.5 = P (1 + 15/100)

⇒ $8912.5 = P (100 + 15/100)

⇒ $8912.5 = P × 115/100

⇒ P × 115/100 = $8912.5

⇒ P = 8912.5/115/100

⇒ P = 8912.5 × 100/115

⇒ P = 8912.5 × 100/115

⇒ P = 891250/115

⇒ P = $7750

Thus, the sum borrowed (P) = $7750 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 8912.5, then the Principal = 100/115 × 8912.5

= 100 × 8912.5/115

= 891250/115

= 7750

Thus, Principal = $7750

Thus, the sum borrowed = $7750 Answer


Similar Questions

(1) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $8428 to clear the loan, then find the time period of the loan.

(2) Find the amount to be paid if Robert borrowed a sum of $5100 at 9% simple interest for 8 years.

(3) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $7546 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 3% simple interest.

(5) Calculate the amount due if Charles borrowed a sum of $3900 at 9% simple interest for 4 years.

(6) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 5% simple interest?

(7) Find the amount to be paid if Jessica borrowed a sum of $5750 at 9% simple interest for 7 years.

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

(9) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 5% simple interest?

(10) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $10595 to clear the loan, then find the time period of the loan.


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