Simple Interest
Math MCQs

Question :    If Margaret paid $4872 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

Correct Answer  $4350

Solution & Explanation

Solution

Given,

Amount (A) = $4872

Rate of Simple Interest (R) = 3%

Time (T) = 4 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

$4872 = P (1 + 3% × 4)

⇒ $4872 = P (1 + ³/₁₀₀ × 4)

⇒ $4872 = P (1 + ^{3 × 4}/₁₀₀)

⇒ $4872 = P (1 + ¹²/₁₀₀)

⇒ $4872 = P (^{100 + 12}/₁₀₀)

⇒ $4872 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $4872

⇒ P = ⁴⁸⁷²/_¹¹²/100

⇒ P = 4872 × ¹⁰⁰/₁₁₂

⇒ P = ^{4872 × 100}/₁₁₂

⇒ P = ⁴⁸⁷²⁰⁰/₁₁₂

⇒ P = $4350

Thus, the sum borrowed (P) = $4350 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 = 3% per annum

Thus, Interest = 3% of principal

⇒ Interest = 3% of 100 = 3

Thus, Simple Interest for 1 year = 3

Calculation of the Amount

Since, in the question, time = 4 years

So, we need to calculate the simple interest for the given time period, which is 4 years

Thus, Simple Interest for 4 years = 4 × Simple Interest for 1 year

= 4 × 3 = 12

Thus, simple interest for 4 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 4872, then the Principal = ¹⁰⁰/₁₁₂ × 4872

= ^{100 × 4872}/₁₁₂

= ⁴⁸⁷²⁰⁰/₁₁₂

= 4350

Thus, Principal = $4350

Thus, the sum borrowed = $4350 Answer

Similar Questions

(1) If John paid $3584 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(2) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 6% simple interest?

(3) If Karen borrowed $3950 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(4) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 4% simple interest?

(5) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 9% simple interest?

(6) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 6% simple interest?

(7) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $7783 to clear the loan, then find the time period of the loan.

(8) Richard had to pay $3924 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(9) Find the amount to be paid if Thomas borrowed a sum of $5800 at 4% simple interest for 8 years.

(10) Calculate the amount due if William borrowed a sum of $3500 at 7% simple interest for 4 years.