Simple Interest
Math MCQs

Question :    Barbara had to pay $3763 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  $3550

Solution & Explanation

Solution

Given,

Amount (A) = $3763

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

$3763 = P (1 + 2% × 3)

⇒ $3763 = P (1 + ²/₁₀₀ × 3)

⇒ $3763 = P (1 + ^{2 × 3}/₁₀₀)

⇒ $3763 = P (1 + ⁶/₁₀₀)

⇒ $3763 = P (^{100 + 6}/₁₀₀)

⇒ $3763 = P × ¹⁰⁶/₁₀₀

⇒ P × ¹⁰⁶/₁₀₀ = $3763

⇒ P = ³⁷⁶³/_¹⁰⁶/100

⇒ P = 3763 × ¹⁰⁰/₁₀₆

⇒ P = ^{3763 × 100}/₁₀₆

⇒ P = ³⁷⁶³⁰⁰/₁₀₆

⇒ P = $3550

Thus, the sum borrowed (P) = $3550 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 3763, then the Principal = ¹⁰⁰/₁₀₆ × 3763

= ^{100 × 3763}/₁₀₆

= ³⁷⁶³⁰⁰/₁₀₆

= 3550

Thus, Principal = $3550

Thus, the sum borrowed = $3550 Answer

Similar Questions

(1) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $10664 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 5% simple interest.

(3) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $9540 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 10% simple interest.

(5) Calculate the amount due if William borrowed a sum of $3500 at 9% simple interest for 4 years.

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

(7) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $7696 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 3% simple interest.

(9) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $9028 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 5% simple interest.