Simple Interest
MCQs Math


Question:     How much loan did Margaret borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6985 to clear it?


Correct Answer  $6350

Solution And Explanation

Solution

Given,

Amount (A) = $6985

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

$6985 = P (1 + 2% × 5)

⇒ $6985 = P (1 + 2/100 × 5)

⇒ $6985 = P (1 + 2 × 5/100)

⇒ $6985 = P (1 + 10/100)

⇒ $6985 = P (100 + 10/100)

⇒ $6985 = P × 110/100

⇒ P × 110/100 = $6985

⇒ P = 6985/110/100

⇒ P = 6985 × 100/110

⇒ P = 6985 × 100/110

⇒ P = 698500/110

⇒ P = $6350

Thus, the sum borrowed (P) = $6350 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 6985, then the Principal = 100/110 × 6985

= 100 × 6985/110

= 698500/110

= 6350

Thus, Principal = $6350

Thus, the sum borrowed = $6350 Answer


Similar Questions

(1) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 7% simple interest?

(2) Calculate the amount due if Linda borrowed a sum of $3350 at 3% simple interest for 3 years.

(3) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $6512 to clear the loan, then find the time period of the loan.

(4) Find the amount to be paid if James borrowed a sum of $5000 at 6% simple interest for 7 years.

(5) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 6% simple interest.

(6) Ashley had to pay $5096 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(7) Michelle had to pay $5544 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(8) David took a loan of $4800 at the rate of 7% simple interest per annum. If he paid an amount of $7824 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due if Mary borrowed a sum of $3050 at 6% simple interest for 3 years.

(10) What amount will be due after 2 years if William borrowed a sum of $3250 at a 4% simple interest?


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