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) In how much time a principal of $3050 will amount to $3660 at a simple interest of 5% per annum?

(2) If Robert paid $3348 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(3) Calculate the amount due if Karen borrowed a sum of $3950 at 5% simple interest for 3 years.

(4) If Jennifer paid $3770 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(5) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $9540 to clear the loan, then find the time period of the loan.

(6) If Kenneth paid $5600 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(7) Find the amount to be paid if Jessica borrowed a sum of $5750 at 4% simple interest for 7 years.

(8) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $10608 to clear the loan, then find the time period of the loan.

(9) Find the amount to be paid if Richard borrowed a sum of $5600 at 2% simple interest for 8 years.

(10) In how much time a principal of $3050 will amount to $3233 at a simple interest of 2% per annum?