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) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $6660 to clear the loan, then find the time period of the loan.

(2) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 4% simple interest?

(3) Robert had to pay $3565 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(4) In how much time a principal of $3000 will amount to $3270 at a simple interest of 3% per annum?

(5) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $11400 to clear the loan, then find the time period of the loan.

(6) How much loan did Robert borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6120 to clear it?

(7) What amount does David have to pay after 5 years if he takes a loan of $3400 at 7% simple interest?

(8) If Betty paid $5100 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 Patricia borrowed a sum of $3150 at 2% simple interest for 4 years.

(10) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $8428 to clear the loan, then find the time period of the loan.