Simple Interest
Math MCQs

Question :    Ashley had to pay $4823 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

Correct Answer  $4550

Solution & Explanation

Solution

Given,

Amount (A) = $4823

Rate of Simple Interest (R) = 2%

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

$4823 = P (1 + 2% × 3)

⇒ $4823 = P (1 + ²/₁₀₀ × 3)

⇒ $4823 = P (1 + ^{2 × 3}/₁₀₀)

⇒ $4823 = P (1 + ⁶/₁₀₀)

⇒ $4823 = P (^{100 + 6}/₁₀₀)

⇒ $4823 = P × ¹⁰⁶/₁₀₀

⇒ P × ¹⁰⁶/₁₀₀ = $4823

⇒ P = ⁴⁸²³/_¹⁰⁶/100

⇒ P = 4823 × ¹⁰⁰/₁₀₆

⇒ P = ^{4823 × 100}/₁₀₆

⇒ P = ⁴⁸²³⁰⁰/₁₀₆

⇒ P = $4550

Thus, the sum borrowed (P) = $4550 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 = 2% per annum

Thus, Interest = 2% of principal

⇒ Interest = 2% of 100 = 2

Thus, Simple Interest for 1 year = 2

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 × 2 = 6

Thus, simple interest for 3 years = 6

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 6 = 106

Calculation of the Principal

Now,

∵ If the Amount is 106, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₀₆

∴ If the Amount is 4823, then the Principal = ¹⁰⁰/₁₀₆ × 4823

= ^{100 × 4823}/₁₀₆

= ⁴⁸²³⁰⁰/₁₀₆

= 4550

Thus, Principal = $4550

Thus, the sum borrowed = $4550 Answer

Similar Questions

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

(2) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $12420 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 5% simple interest.

(4) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 7% simple interest?

(5) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 9% simple interest?

(6) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 6% simple interest for 4 years.

(7) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $9240 to clear the loan, then find the time period of the loan.

(8) If Charles borrowed $3900 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(9) If Ashley paid $5096 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(10) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $9180 to clear the loan, then find the time period of the loan.