Simple Interest
Math MCQs

Question :    John had to pay $3392 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

Correct Answer  $3200

Solution & Explanation

Solution

Given,

Amount (A) = $3392

Rate of Simple Interest (R) = 2%

Time (T) = 3 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

$3392 = P (1 + 2% × 3)

⇒ $3392 = P (1 + ²/₁₀₀ × 3)

⇒ $3392 = P (1 + ^{2 × 3}/₁₀₀)

⇒ $3392 = P (1 + ⁶/₁₀₀)

⇒ $3392 = P (^{100 + 6}/₁₀₀)

⇒ $3392 = P × ¹⁰⁶/₁₀₀

⇒ P × ¹⁰⁶/₁₀₀ = $3392

⇒ P = ³³⁹²/_¹⁰⁶/100

⇒ P = 3392 × ¹⁰⁰/₁₀₆

⇒ P = ^{3392 × 100}/₁₀₆

⇒ P = ³³⁹²⁰⁰/₁₀₆

⇒ P = $3200

Thus, the sum borrowed (P) = $3200 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 = 3 years

So, we need to calculate the simple interest for the given time period, which is 3 years

Thus, Simple Interest for 3 years = 3 × Simple Interest for 1 year

= 3 × 2 = 6

Thus, simple interest for 3 years = 6

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 6 = 106

Calculation of the Principal

Now,

∵ If the Amount is 106, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₀₆

∴ If the Amount is 3392, then the Principal = ¹⁰⁰/₁₀₆ × 3392

= ^{100 × 3392}/₁₀₆

= ³³⁹²⁰⁰/₁₀₆

= 3200

Thus, Principal = $3200

Thus, the sum borrowed = $3200 Answer

Similar Questions

(1) How much loan did Andrew borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8500 to clear it?

(2) What amount does John have to pay after 5 years if he takes a loan of $3200 at 4% simple interest?

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

(4) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $6664 to clear the loan, then find the time period of the loan.

(5) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $9600 to clear the loan, then find the time period of the loan.

(6) How much loan did Matthew borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6820 to clear it?

(7) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $9460 to clear the loan, then find the time period of the loan.

(8) If Elizabeth paid $4140 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(9) Calculate the amount due if Robert borrowed a sum of $3100 at 4% simple interest for 3 years.

(10) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $10980 to clear the loan, then find the time period of the loan.