Simple Interest
Math MCQs

Question :    If Christopher paid $4640 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

Correct Answer  $4000

Solution & Explanation

Solution

Given,

Amount (A) = $4640

Rate of Simple Interest (R) = 4%

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

$4640 = P (1 + 4% × 4)

⇒ $4640 = P (1 + ⁴/₁₀₀ × 4)

⇒ $4640 = P (1 + ^{4 × 4}/₁₀₀)

⇒ $4640 = P (1 + ¹⁶/₁₀₀)

⇒ $4640 = P (^{100 + 16}/₁₀₀)

⇒ $4640 = P × ¹¹⁶/₁₀₀

⇒ P × ¹¹⁶/₁₀₀ = $4640

⇒ P = ⁴⁶⁴⁰/_¹¹⁶/100

⇒ P = 4640 × ¹⁰⁰/₁₁₆

⇒ P = ^{4640 × 100}/₁₁₆

⇒ P = ⁴⁶⁴⁰⁰⁰/₁₁₆

⇒ 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 = 4% per annum

Thus, Interest = 4% of principal

⇒ Interest = 4% of 100 = 4

Thus, Simple Interest for 1 year = 4

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 × 4 = 16

Thus, simple interest for 4 years = 16

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 16 = 116

Calculation of the Principal

Now,

∵ If the Amount is 116, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₆

∴ If the Amount is 4640, then the Principal = ¹⁰⁰/₁₁₆ × 4640

= ^{100 × 4640}/₁₁₆

= ⁴⁶⁴⁰⁰⁰/₁₁₆

= 4000

Thus, Principal = $4000

Thus, the sum borrowed = $4000 Answer

Similar Questions

(1) Calculate the amount due if Joseph borrowed a sum of $3700 at 3% simple interest for 3 years.

(2) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $10200 to clear the loan, then find the time period of the loan.

(3) Find the amount to be paid if Thomas borrowed a sum of $5800 at 4% simple interest for 8 years.

(4) Find the amount to be paid if David borrowed a sum of $5400 at 10% simple interest for 7 years.

(5) Calculate the amount due if Barbara borrowed a sum of $3550 at 2% simple interest for 4 years.

(6) Find the amount to be paid if James borrowed a sum of $5000 at 7% simple interest for 7 years.

(7) Calculate the amount due if Charles borrowed a sum of $3900 at 7% simple interest for 4 years.

(8) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $8550 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 6% simple interest.

(10) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $10317 to clear the loan, then find the time period of the loan.