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 if Charles borrowed a sum of $3900 at 9% simple interest for 4 years.

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

(3) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $7140 to clear the loan, then find the time period of the loan.

(4) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $7520 to clear the loan, then find the time period of the loan.

(5) Find the amount to be paid if Christopher borrowed a sum of $6000 at 6% simple interest for 8 years.

(6) Linda had to pay $3752 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(7) Karen had to pay $4305.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(8) Find the amount to be paid if Patricia borrowed a sum of $5150 at 6% simple interest for 8 years.

(9) If Karen borrowed $3950 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(10) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 5% simple interest?