Simple Interest
Math MCQs

Question :    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.

Correct Answer  $5000

Solution & Explanation

Solution

Given,

Amount (A) = $5600

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

$5600 = P (1 + 3% × 4)

⇒ $5600 = P (1 + ³/₁₀₀ × 4)

⇒ $5600 = P (1 + ^{3 × 4}/₁₀₀)

⇒ $5600 = P (1 + ¹²/₁₀₀)

⇒ $5600 = P (^{100 + 12}/₁₀₀)

⇒ $5600 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $5600

⇒ P = ⁵⁶⁰⁰/_¹¹²/100

⇒ P = 5600 × ¹⁰⁰/₁₁₂

⇒ P = ^{5600 × 100}/₁₁₂

⇒ P = ⁵⁶⁰⁰⁰⁰/₁₁₂

⇒ P = $5000

Thus, the sum borrowed (P) = $5000 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 5600, then the Principal = ¹⁰⁰/₁₁₂ × 5600

= ^{100 × 5600}/₁₁₂

= ⁵⁶⁰⁰⁰⁰/₁₁₂

= 5000

Thus, Principal = $5000

Thus, the sum borrowed = $5000 Answer

Similar Questions

(1) If David borrowed $3400 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(2) In how much time a principal of $3150 will amount to $3937.5 at a simple interest of 5% per annum?

(3) How much loan did Kevin borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7810 to clear it?

(4) How much loan did Carol borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8107.5 to clear it?

(5) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 9% simple interest.

(6) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 9% simple interest.

(7) Find the amount to be paid if Charles borrowed a sum of $5900 at 6% simple interest for 8 years.

(8) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $7820 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due if Mary borrowed a sum of $3050 at 5% simple interest for 3 years.

(10) If Michael borrowed $3300 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.