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) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 3% simple interest.

(2) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $8493 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 9% simple interest.

(4) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 7% simple interest?

(5) If Donna paid $5432 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(6) Find the amount to be paid if Thomas borrowed a sum of $5800 at 8% simple interest for 7 years.

(7) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 8% simple interest.

(8) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 10% simple interest.

(9) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $8094 to clear the loan, then find the time period of the loan.

(10) Find the amount to be paid if Christopher borrowed a sum of $6000 at 4% simple interest for 8 years.