Simple Interest
Math MCQs

Question :    Michelle had to pay $5544 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  $4950

Solution & Explanation

Solution

Given,

Amount (A) = $5544

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

$5544 = P (1 + 4% × 3)

⇒ $5544 = P (1 + ⁴/₁₀₀ × 3)

⇒ $5544 = P (1 + ^{4 × 3}/₁₀₀)

⇒ $5544 = P (1 + ¹²/₁₀₀)

⇒ $5544 = P (^{100 + 12}/₁₀₀)

⇒ $5544 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $5544

⇒ P = ⁵⁵⁴⁴/_¹¹²/100

⇒ P = 5544 × ¹⁰⁰/₁₁₂

⇒ P = ^{5544 × 100}/₁₁₂

⇒ P = ⁵⁵⁴⁴⁰⁰/₁₁₂

⇒ P = $4950

Thus, the sum borrowed (P) = $4950 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 5544, then the Principal = ¹⁰⁰/₁₁₂ × 5544

= ^{100 × 5544}/₁₁₂

= ⁵⁵⁴⁴⁰⁰/₁₁₂

= 4950

Thus, Principal = $4950

Thus, the sum borrowed = $4950 Answer

Similar Questions

(1) Calculate the amount due if Charles borrowed a sum of $3900 at 5% simple interest for 3 years.

(2) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $7700 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due if Charles borrowed a sum of $3900 at 2% simple interest for 4 years.

(4) Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $10824 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 10% simple interest.

(6) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $9400 to clear the loan, then find the time period of the loan.

(7) Find the amount to be paid if Barbara borrowed a sum of $5550 at 2% simple interest for 8 years.

(8) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 3% simple interest.

(9) Find the amount to be paid if William borrowed a sum of $5500 at 6% simple interest for 7 years.

(10) Find the amount to be paid if Susan borrowed a sum of $5650 at 4% simple interest for 7 years.