Simple Interest
Math MCQs

Question :    David had to pay $3808 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

Correct Answer  $3400

Solution & Explanation

Solution

Given,

Amount (A) = $3808

Rate of Simple Interest (R) = 4%

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

$3808 = P (1 + 4% × 3)

⇒ $3808 = P (1 + ⁴/₁₀₀ × 3)

⇒ $3808 = P (1 + ^{4 × 3}/₁₀₀)

⇒ $3808 = P (1 + ¹²/₁₀₀)

⇒ $3808 = P (^{100 + 12}/₁₀₀)

⇒ $3808 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $3808

⇒ P = ³⁸⁰⁸/_¹¹²/100

⇒ P = 3808 × ¹⁰⁰/₁₁₂

⇒ P = ^{3808 × 100}/₁₁₂

⇒ P = ³⁸⁰⁸⁰⁰/₁₁₂

⇒ P = $3400

Thus, the sum borrowed (P) = $3400 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 = 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 × 4 = 12

Thus, simple interest for 3 years = 12

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 12 = 112

Calculation of the Principal

Now,

∵ If the Amount is 112, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₂

∴ If the Amount is 3808, then the Principal = ¹⁰⁰/₁₁₂ × 3808

= ^{100 × 3808}/₁₁₂

= ³⁸⁰⁸⁰⁰/₁₁₂

= 3400

Thus, Principal = $3400

Thus, the sum borrowed = $3400 Answer

Similar Questions

(1) How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9750 to clear it?

(2) How much loan did Deborah borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8567.5 to clear it?

(3) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $10595 to clear the loan, then find the time period of the loan.

(4) How much loan did Elizabeth borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5995 to clear it?

(5) Calculate the amount due if James borrowed a sum of $3000 at 6% simple interest for 4 years.

(6) Jennifer took a loan of $4500 at the rate of 10% simple interest per annum. If he paid an amount of $7650 to clear the loan, then find the time period of the loan.

(7) In how much time a principal of $3150 will amount to $3780 at a simple interest of 4% per annum?

(8) How much loan did Amanda borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7865 to clear it?

(9) Find the amount to be paid if John borrowed a sum of $5200 at 5% simple interest for 8 years.

(10) Calculate the amount due if Jessica borrowed a sum of $3750 at 7% simple interest for 4 years.