Simple Interest
Math MCQs

Question :    If Charles paid $4368 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

Correct Answer  $3900

Solution & Explanation

Solution

Given,

Amount (A) = $4368

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

$4368 = P (1 + 3% × 4)

⇒ $4368 = P (1 + ³/₁₀₀ × 4)

⇒ $4368 = P (1 + ^{3 × 4}/₁₀₀)

⇒ $4368 = P (1 + ¹²/₁₀₀)

⇒ $4368 = P (^{100 + 12}/₁₀₀)

⇒ $4368 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $4368

⇒ P = ⁴³⁶⁸/_¹¹²/100

⇒ P = 4368 × ¹⁰⁰/₁₁₂

⇒ P = ^{4368 × 100}/₁₁₂

⇒ P = ⁴³⁶⁸⁰⁰/₁₁₂

⇒ P = $3900

Thus, the sum borrowed (P) = $3900 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 4368, then the Principal = ¹⁰⁰/₁₁₂ × 4368

= ^{100 × 4368}/₁₁₂

= ⁴³⁶⁸⁰⁰/₁₁₂

= 3900

Thus, Principal = $3900

Thus, the sum borrowed = $3900 Answer

Similar Questions

(1) If Steven paid $5336 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(2) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 10% simple interest?

(3) Karen had to pay $4542.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(4) Anthony had to pay $4558 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(5) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 9% simple interest.

(6) Find the amount to be paid if Patricia borrowed a sum of $5150 at 10% simple interest for 8 years.

(7) If Donald paid $5220 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(8) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 9% simple interest.

(9) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $9840 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 2% simple interest.