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) In how much time a principal of $3000 will amount to $3600 at a simple interest of 5% per annum?

(2) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 5% simple interest for 7 years.

(3) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 6% simple interest.

(4) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 10% simple interest?

(5) Find the amount to be paid if Richard borrowed a sum of $5600 at 8% simple interest for 8 years.

(6) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $11520 to clear the loan, then find the time period of the loan.

(7) How much loan did Barbara borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6937.5 to clear it?

(8) In how much time a principal of $3150 will amount to $3528 at a simple interest of 3% per annum?

(9) Find the amount to be paid if Michael borrowed a sum of $5300 at 10% simple interest for 7 years.

(10) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $8772 to clear the loan, then find the time period of the loan.