Simple Interest
Math MCQs

Question :    If Ashley paid $4914 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

Correct Answer  $4550

Solution & Explanation

Solution

Given,

Amount (A) = $4914

Rate of Simple Interest (R) = 2%

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

$4914 = P (1 + 2% × 4)

⇒ $4914 = P (1 + ²/₁₀₀ × 4)

⇒ $4914 = P (1 + ^{2 × 4}/₁₀₀)

⇒ $4914 = P (1 + ⁸/₁₀₀)

⇒ $4914 = P (^{100 + 8}/₁₀₀)

⇒ $4914 = P × ¹⁰⁸/₁₀₀

⇒ P × ¹⁰⁸/₁₀₀ = $4914

⇒ P = ⁴⁹¹⁴/_¹⁰⁸/100

⇒ P = 4914 × ¹⁰⁰/₁₀₈

⇒ P = ^{4914 × 100}/₁₀₈

⇒ P = ⁴⁹¹⁴⁰⁰/₁₀₈

⇒ 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 = 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 × 2 = 8

Thus, simple interest for 4 years = 8

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 8 = 108

Calculation of the Principal

Now,

∵ If the Amount is 108, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₀₈

∴ If the Amount is 4914, then the Principal = ¹⁰⁰/₁₀₈ × 4914

= ^{100 × 4914}/₁₀₈

= ⁴⁹¹⁴⁰⁰/₁₀₈

= 4550

Thus, Principal = $4550

Thus, the sum borrowed = $4550 Answer

Similar Questions

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

(2) Calculate the amount due if John borrowed a sum of $3200 at 8% simple interest for 4 years.

(3) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 9% simple interest.

(4) How much loan did Mary borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5807.5 to clear it?

(5) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $10640 to clear the loan, then find the time period of the loan.

(6) If Paul paid $5264 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(7) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 6% simple interest?

(8) Find the amount to be paid if Christopher borrowed a sum of $6000 at 4% simple interest for 8 years.

(9) Calculate the amount due if William borrowed a sum of $3500 at 9% simple interest for 3 years.

(10) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $7616 to clear the loan, then find the time period of the loan.