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Simple Interest
Math MCQs


Question :    How much loan did George borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8760 to clear it?


Correct Answer  $7300

Solution & Explanation

Solution

Given,

Amount (A) = $8760

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

$8760 = P (1 + 4% × 5)

⇒ $8760 = P (1 + 4/100 × 5)

⇒ $8760 = P (1 + 4 × 5/100)

⇒ $8760 = P (1 + 20/100)

⇒ $8760 = P (100 + 20/100)

⇒ $8760 = P × 120/100

⇒ P × 120/100 = $8760

⇒ P = 8760/120/100

⇒ P = 8760 × 100/120

⇒ P = 8760 × 100/120

⇒ P = 876000/120

⇒ P = $7300

Thus, the sum borrowed (P) = $7300 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 8760, then the Principal = 100/120 × 8760

= 100 × 8760/120

= 876000/120

= 7300

Thus, Principal = $7300

Thus, the sum borrowed = $7300 Answer


Similar Questions

(1) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $5920 to clear the loan, then find the time period of the loan.

(2) Find the amount to be paid if John borrowed a sum of $5200 at 5% simple interest for 7 years.

(3) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $10000 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 2% simple interest.

(5) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 7% simple interest.

(6) How much loan did Kimberly borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8312.5 to clear it?

(7) What amount does John have to pay after 6 years if he takes a loan of $3200 at 2% simple interest?

(8) If Joseph borrowed $3700 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

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

(10) Find the amount to be paid if Sarah borrowed a sum of $5850 at 2% simple interest for 8 years.