Simple Interest
Math MCQs

Question :    If Patricia paid $3528 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

Correct Answer  $3150

Solution & Explanation

Solution

Given,

Amount (A) = $3528

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

$3528 = P (1 + 3% × 4)

⇒ $3528 = P (1 + ³/₁₀₀ × 4)

⇒ $3528 = P (1 + ^{3 × 4}/₁₀₀)

⇒ $3528 = P (1 + ¹²/₁₀₀)

⇒ $3528 = P (^{100 + 12}/₁₀₀)

⇒ $3528 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $3528

⇒ P = ³⁵²⁸/_¹¹²/100

⇒ P = 3528 × ¹⁰⁰/₁₁₂

⇒ P = ^{3528 × 100}/₁₁₂

⇒ P = ³⁵²⁸⁰⁰/₁₁₂

⇒ P = $3150

Thus, the sum borrowed (P) = $3150 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 3528, then the Principal = ¹⁰⁰/₁₁₂ × 3528

= ^{100 × 3528}/₁₁₂

= ³⁵²⁸⁰⁰/₁₁₂

= 3150

Thus, Principal = $3150

Thus, the sum borrowed = $3150 Answer

Similar Questions

(1) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 2% simple interest.

(2) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $10758 to clear the loan, then find the time period of the loan.

(3) If David paid $3672 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(4) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $6256 to clear the loan, then find the time period of the loan.

(5) Sandra had to pay $4717 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(6) Calculate the amount due if Robert borrowed a sum of $3100 at 2% simple interest for 4 years.

(7) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $10626 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due if James borrowed a sum of $3000 at 4% simple interest for 3 years.

(9) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $7252 to clear the loan, then find the time period of the loan.

(10) Find the amount to be paid if Barbara borrowed a sum of $5550 at 2% simple interest for 8 years.