Simple Interest
Math MCQs

Question :    If Christopher paid $4480 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

Correct Answer  $4000

Solution & Explanation

Solution

Given,

Amount (A) = $4480

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

$4480 = P (1 + 3% × 4)

⇒ $4480 = P (1 + ³/₁₀₀ × 4)

⇒ $4480 = P (1 + ^{3 × 4}/₁₀₀)

⇒ $4480 = P (1 + ¹²/₁₀₀)

⇒ $4480 = P (^{100 + 12}/₁₀₀)

⇒ $4480 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $4480

⇒ P = ⁴⁴⁸⁰/_¹¹²/100

⇒ P = 4480 × ¹⁰⁰/₁₁₂

⇒ P = ^{4480 × 100}/₁₁₂

⇒ P = ⁴⁴⁸⁰⁰⁰/₁₁₂

⇒ P = $4000

Thus, the sum borrowed (P) = $4000 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 4480, then the Principal = ¹⁰⁰/₁₁₂ × 4480

= ^{100 × 4480}/₁₁₂

= ⁴⁴⁸⁰⁰⁰/₁₁₂

= 4000

Thus, Principal = $4000

Thus, the sum borrowed = $4000 Answer

Similar Questions

(1) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 10% simple interest?

(2) Find the amount to be paid if William borrowed a sum of $5500 at 8% simple interest for 7 years.

(3) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 6% simple interest?

(4) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $10320 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due if Sarah borrowed a sum of $3850 at 4% simple interest for 4 years.

(6) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 8% simple interest?

(7) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.

(8) Kenneth had to pay $5600 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(9) Calculate the amount due if Jessica borrowed a sum of $3750 at 5% simple interest for 3 years.

(10) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.