Simple Interest
MCQs Math


Question:     How much loan did Carol borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8460 to clear it?


Correct Answer  $7050

Solution And Explanation

Solution

Given,

Amount (A) = $8460

Rate of Simple Interest (R) = 4%

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

$8460 = P (1 + 4% × 5)

⇒ $8460 = P (1 + 4/100 × 5)

⇒ $8460 = P (1 + 4 × 5/100)

⇒ $8460 = P (1 + 20/100)

⇒ $8460 = P (100 + 20/100)

⇒ $8460 = P × 120/100

⇒ P × 120/100 = $8460

⇒ P = 8460/120/100

⇒ P = 8460 × 100/120

⇒ P = 8460 × 100/120

⇒ P = 846000/120

⇒ P = $7050

Thus, the sum borrowed (P) = $7050 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 = 4% per annum

Thus, Interest = 4% of principal

⇒ Interest = 4% of 100 = 4

Thus, Simple Interest for 1 year = 4

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 × 4 = 20

Thus, simple interest for 5 years = 20

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 20 = 120

Calculation of the Principal

Now,

∵ If the Amount is 120, then the Principal = 100

∴ If the Amount is 1, then the Principal = 100/120

∴ If the Amount is 8460, then the Principal = 100/120 × 8460

= 100 × 8460/120

= 846000/120

= 7050

Thus, Principal = $7050

Thus, the sum borrowed = $7050 Answer


Similar Questions

(1) If Charles borrowed $3900 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(2) Charles had to pay $4368 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(3) Find the amount to be paid if Michael borrowed a sum of $5300 at 6% simple interest for 7 years.

(4) Find the amount to be paid if Susan borrowed a sum of $5650 at 3% simple interest for 7 years.

(5) Find the amount to be paid if Christopher borrowed a sum of $6000 at 5% simple interest for 7 years.

(6) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 5% simple interest?

(7) How much loan did James borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6000 to clear it?

(8) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 4% simple interest.

(9) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $10140 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due if Mary borrowed a sum of $3050 at 8% simple interest for 4 years.


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