Simple Interest
Math MCQs

Question :    Charles had to pay $4368 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  $3900

Solution & Explanation

Solution

Given,

Amount (A) = $4368

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

$4368 = P (1 + 4% × 3)

⇒ $4368 = P (1 + ⁴/₁₀₀ × 3)

⇒ $4368 = P (1 + ^{4 × 3}/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 = 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 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) Find the amount to be paid if Barbara borrowed a sum of $5550 at 4% simple interest for 7 years.

(2) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 6% simple interest?

(3) How much loan did Patricia borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6437.5 to clear it?

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

(5) Calculate the amount due if Thomas borrowed a sum of $3800 at 3% simple interest for 4 years.

(6) Barbara had to pay $3763 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(7) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 5% simple interest?

(8) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 6% simple interest?

(9) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $10472 to clear the loan, then find the time period of the loan.

(10) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $6854 to clear the loan, then find the time period of the loan.