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) If Anthony paid $4816 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(2) If Sandra paid $5162 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(3) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 2% simple interest.

(4) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 10% simple interest for 8 years.

(5) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 3% simple interest.

(6) Calculate the amount due if David borrowed a sum of $3400 at 2% simple interest for 3 years.

(7) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $8084 to clear the loan, then find the time period of the loan.

(8) Find the amount to be paid if Jessica borrowed a sum of $5750 at 9% simple interest for 7 years.

(9) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $8470 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due if Richard borrowed a sum of $3600 at 5% simple interest for 4 years.