Simple Interest
Math MCQs

Question :    Margaret had to pay $4872 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  $4350

Solution & Explanation

Solution

Given,

Amount (A) = $4872

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

$4872 = P (1 + 4% × 3)

⇒ $4872 = P (1 + ⁴/₁₀₀ × 3)

⇒ $4872 = P (1 + ^{4 × 3}/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 = 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 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) In how much time a principal of $3050 will amount to $3233 at a simple interest of 2% per annum?

(2) Calculate the amount due if Patricia borrowed a sum of $3150 at 3% simple interest for 3 years.

(3) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $6160 to clear the loan, then find the time period of the loan.

(4) How much loan did Patricia borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5922.5 to clear it?

(5) If Robert paid $3720 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(6) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6683 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due if James borrowed a sum of $3000 at 2% simple interest for 3 years.

(8) Find the amount to be paid if Patricia borrowed a sum of $5150 at 8% simple interest for 8 years.

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

(10) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 3% simple interest.