Simple Interest
Math MCQs

Question :    If Anthony paid $4816 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

Correct Answer  $4300

Solution & Explanation

Solution

Given,

Amount (A) = $4816

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

$4816 = P (1 + 3% × 4)

⇒ $4816 = P (1 + ³/₁₀₀ × 4)

⇒ $4816 = P (1 + ^{3 × 4}/₁₀₀)

⇒ $4816 = P (1 + ¹²/₁₀₀)

⇒ $4816 = P (^{100 + 12}/₁₀₀)

⇒ $4816 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $4816

⇒ P = ⁴⁸¹⁶/_¹¹²/100

⇒ P = 4816 × ¹⁰⁰/₁₁₂

⇒ P = ^{4816 × 100}/₁₁₂

⇒ P = ⁴⁸¹⁶⁰⁰/₁₁₂

⇒ P = $4300

Thus, the sum borrowed (P) = $4300 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 4816, then the Principal = ¹⁰⁰/₁₁₂ × 4816

= ^{100 × 4816}/₁₁₂

= ⁴⁸¹⁶⁰⁰/₁₁₂

= 4300

Thus, Principal = $4300

Thus, the sum borrowed = $4300 Answer

Similar Questions

(1) Find the amount to be paid if Christopher borrowed a sum of $6000 at 7% simple interest for 7 years.

(2) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 7% simple interest.

(3) If Jessica borrowed $3750 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(4) Find the amount to be paid if Christopher borrowed a sum of $6000 at 4% simple interest for 7 years.

(5) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $6622 to clear the loan, then find the time period of the loan.

(6) Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $10780 to clear the loan, then find the time period of the loan.

(7) Karen had to pay $4542.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(8) If Mary borrowed $3050 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(9) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 10% simple interest.

(10) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 10% simple interest.