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 9 years if Richard borrowed a sum of $5600 at a rate of 4% simple interest.

(2) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 10% simple interest.

(3) How much loan did Joseph borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6840 to clear it?

(4) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $8804 to clear the loan, then find the time period of the loan.

(5) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 10% simple interest?

(6) Calculate the amount due if Robert borrowed a sum of $3100 at 5% simple interest for 4 years.

(7) How much loan did Robert borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5610 to clear it?

(8) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $10030 to clear the loan, then find the time period of the loan.

(9) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $7009 to clear the loan, then find the time period of the loan.

(10) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $10296 to clear the loan, then find the time period of the loan.