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 10% simple interest.

(2) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $7854 to clear the loan, then find the time period of the loan.

(3) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $7396 to clear the loan, then find the time period of the loan.

(4) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 5% simple interest?

(5) What amount does James have to pay after 6 years if he takes a loan of $3000 at 8% simple interest?

(6) How much loan did Melissa borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8820 to clear it?

(7) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 2% simple interest?

(8) Calculate the amount due if James borrowed a sum of $3000 at 9% simple interest for 4 years.

(9) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $9176 to clear the loan, then find the time period of the loan.

(10) If Kimberly paid $5580 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.