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) Calculate the amount due if Michael borrowed a sum of $3300 at 9% simple interest for 3 years.

(2) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $8704 to clear the loan, then find the time period of the loan.

(3) Find the amount to be paid if David borrowed a sum of $5400 at 2% simple interest for 8 years.

(4) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 3% simple interest?

(5) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $8360 to clear the loan, then find the time period of the loan.

(6) If Joshua paid $5292 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(7) Find the amount to be paid if Michael borrowed a sum of $5300 at 5% simple interest for 8 years.

(8) Calculate the amount due if James borrowed a sum of $3000 at 6% simple interest for 3 years.

(9) Find the amount to be paid if Linda borrowed a sum of $5350 at 3% simple interest for 8 years.

(10) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $10281 to clear the loan, then find the time period of the loan.