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) What amount will be due after 2 years if John borrowed a sum of $3100 at a 9% simple interest?

(2) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $9983 to clear the loan, then find the time period of the loan.

(3) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $11520 to clear the loan, then find the time period of the loan.

(4) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $6560 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 6% simple interest.

(6) What amount will be due after 2 years if William borrowed a sum of $3250 at a 4% simple interest?

(7) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 9% simple interest?

(8) Calculate the amount due if Karen borrowed a sum of $3950 at 7% simple interest for 4 years.

(9) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 5% simple interest?

(10) Joseph had to pay $4144 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.