Simple Interest
Math MCQs

Question :    Michael had to pay $3696 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

Correct Answer  $3300

Solution & Explanation

Solution

Given,

Amount (A) = $3696

Rate of Simple Interest (R) = 4%

Time (T) = 3 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 + 4% × 3)

⇒ $3696 = P (1 + ⁴/₁₀₀ × 3)

⇒ $3696 = P (1 + ^{4 × 3}/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 = 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 = 3 years

So, we need to calculate the simple interest for the given time period, which is 3 years

Thus, Simple Interest for 3 years = 3 × Simple Interest for 1 year

= 3 × 4 = 12

Thus, simple interest for 3 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) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 9% simple interest.

(2) Find the amount to be paid if Sarah borrowed a sum of $5850 at 3% simple interest for 8 years.

(3) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 2% simple interest.

(4) Calculate the amount due if Patricia borrowed a sum of $3150 at 3% simple interest for 3 years.

(5) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $11040 to clear the loan, then find the time period of the loan.

(6) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $7544 to clear the loan, then find the time period of the loan.

(7) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 9% simple interest for 7 years.

(8) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $8436 to clear the loan, then find the time period of the loan.

(9) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 2% simple interest?

(10) What amount will be due after 2 years if William borrowed a sum of $3250 at a 9% simple interest?