Simple Interest
Math MCQs

Question :    Patricia had to pay $3339 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

Correct Answer  $3150

Solution & Explanation

Solution

Given,

Amount (A) = $3339

Rate of Simple Interest (R) = 2%

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

$3339 = P (1 + 2% × 3)

⇒ $3339 = P (1 + ²/₁₀₀ × 3)

⇒ $3339 = P (1 + ^{2 × 3}/₁₀₀)

⇒ $3339 = P (1 + ⁶/₁₀₀)

⇒ $3339 = P (^{100 + 6}/₁₀₀)

⇒ $3339 = P × ¹⁰⁶/₁₀₀

⇒ P × ¹⁰⁶/₁₀₀ = $3339

⇒ P = ³³³⁹/_¹⁰⁶/100

⇒ P = 3339 × ¹⁰⁰/₁₀₆

⇒ P = ^{3339 × 100}/₁₀₆

⇒ P = ³³³⁹⁰⁰/₁₀₆

⇒ P = $3150

Thus, the sum borrowed (P) = $3150 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 = 2% per annum

Thus, Interest = 2% of principal

⇒ Interest = 2% of 100 = 2

Thus, Simple Interest for 1 year = 2

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 × 2 = 6

Thus, simple interest for 3 years = 6

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 6 = 106

Calculation of the Principal

Now,

∵ If the Amount is 106, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₀₆

∴ If the Amount is 3339, then the Principal = ¹⁰⁰/₁₀₆ × 3339

= ^{100 × 3339}/₁₀₆

= ³³³⁹⁰⁰/₁₀₆

= 3150

Thus, Principal = $3150

Thus, the sum borrowed = $3150 Answer

Similar Questions

(1) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $6705 to clear the loan, then find the time period of the loan.

(2) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 2% simple interest?

(3) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $6240 to clear the loan, then find the time period of the loan.

(4) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $10626 to clear the loan, then find the time period of the loan.

(5) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 7% simple interest?

(6) Calculate the amount due if William borrowed a sum of $3500 at 9% simple interest for 3 years.

(7) Find the amount to be paid if Sarah borrowed a sum of $5850 at 3% simple interest for 7 years.

(8) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $6552 to clear the loan, then find the time period of the loan.

(9) Mark had to pay $5060 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(10) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 5% simple interest.