Simple Interest
Math MCQs

Question :    If Michael paid $3696 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

Correct Answer  $3300

Solution & Explanation

Solution

Given,

Amount (A) = $3696

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

$3696 = P (1 + 3% × 4)

⇒ $3696 = P (1 + ³/₁₀₀ × 4)

⇒ $3696 = P (1 + ^{3 × 4}/₁₀₀)

⇒ $3696 = P (1 + ¹²/₁₀₀)

⇒ $3696 = P (^{100 + 12}/₁₀₀)

⇒ $3696 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $3696

⇒ P = ³⁶⁹⁶/_¹¹²/100

⇒ P = 3696 × ¹⁰⁰/₁₁₂

⇒ P = ^{3696 × 100}/₁₁₂

⇒ P = ³⁶⁹⁶⁰⁰/₁₁₂

⇒ P = $3300

Thus, the sum borrowed (P) = $3300 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 3696, then the Principal = ¹⁰⁰/₁₁₂ × 3696

= ^{100 × 3696}/₁₁₂

= ³⁶⁹⁶⁰⁰/₁₁₂

= 3300

Thus, Principal = $3300

Thus, the sum borrowed = $3300 Answer

Similar Questions

(1) Find the amount to be paid if James borrowed a sum of $5000 at 9% simple interest for 7 years.

(2) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $7480 to clear the loan, then find the time period of the loan.

(3) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $7696 to clear the loan, then find the time period of the loan.

(4) Find the amount to be paid if James borrowed a sum of $5000 at 3% simple interest for 7 years.

(5) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 6% simple interest?

(6) Calculate the amount due if James borrowed a sum of $3000 at 9% simple interest for 4 years.

(7) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $6468 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due if Michael borrowed a sum of $3300 at 8% simple interest for 4 years.

(9) In how much time a principal of $3150 will amount to $3654 at a simple interest of 4% per annum?

(10) Anthony had to pay $4945 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.