Simple Interest
Math MCQs

Question :    Richard had to pay $4032 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  $3600

Solution & Explanation

Solution

Given,

Amount (A) = $4032

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

$4032 = P (1 + 4% × 3)

⇒ $4032 = P (1 + ⁴/₁₀₀ × 3)

⇒ $4032 = P (1 + ^{4 × 3}/₁₀₀)

⇒ $4032 = P (1 + ¹²/₁₀₀)

⇒ $4032 = P (^{100 + 12}/₁₀₀)

⇒ $4032 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $4032

⇒ P = ⁴⁰³²/_¹¹²/100

⇒ P = 4032 × ¹⁰⁰/₁₁₂

⇒ P = ^{4032 × 100}/₁₁₂

⇒ P = ⁴⁰³²⁰⁰/₁₁₂

⇒ P = $3600

Thus, the sum borrowed (P) = $3600 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 4032, then the Principal = ¹⁰⁰/₁₁₂ × 4032

= ^{100 × 4032}/₁₁₂

= ⁴⁰³²⁰⁰/₁₁₂

= 3600

Thus, Principal = $3600

Thus, the sum borrowed = $3600 Answer

Similar Questions

(1) Find the amount to be paid if Thomas borrowed a sum of $5800 at 9% simple interest for 7 years.

(2) Calculate the amount due if Joseph borrowed a sum of $3700 at 10% simple interest for 4 years.

(3) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $9454 to clear the loan, then find the time period of the loan.

(4) Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $7238 to clear the loan, then find the time period of the loan.

(5) Find the amount to be paid if Sarah borrowed a sum of $5850 at 4% simple interest for 7 years.

(6) Calculate the amount due if Christopher borrowed a sum of $4000 at 3% simple interest for 3 years.

(7) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $8624 to clear the loan, then find the time period of the loan.

(8) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $7854 to clear the loan, then find the time period of the loan.

(9) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $9204 to clear the loan, then find the time period of the loan.

(10) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $9180 to clear the loan, then find the time period of the loan.