Simple Interest
Math MCQs

Question :    Barbara had to pay $3869.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

Correct Answer  $3550

Solution & Explanation

Solution

Given,

Amount (A) = $3869.5

Rate of Simple Interest (R) = 3%

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

$3869.5 = P (1 + 3% × 3)

⇒ $3869.5 = P (1 + ³/₁₀₀ × 3)

⇒ $3869.5 = P (1 + ^{3 × 3}/₁₀₀)

⇒ $3869.5 = P (1 + ⁹/₁₀₀)

⇒ $3869.5 = P (^{100 + 9}/₁₀₀)

⇒ $3869.5 = P × ¹⁰⁹/₁₀₀

⇒ P × ¹⁰⁹/₁₀₀ = $3869.5

⇒ P = ^3869.5/_¹⁰⁹/100

⇒ P = 3869.5 × ¹⁰⁰/₁₀₉

⇒ P = ^{3869.5 × 100}/₁₀₉

⇒ P = ³⁸⁶⁹⁵⁰/₁₀₉

⇒ 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 = 3% per annum

Thus, Interest = 3% of principal

⇒ Interest = 3% of 100 = 3

Thus, Simple Interest for 1 year = 3

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 × 3 = 9

Thus, simple interest for 3 years = 9

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 9 = 109

Calculation of the Principal

Now,

∵ If the Amount is 109, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₀₉

∴ If the Amount is 3869.5, then the Principal = ¹⁰⁰/₁₀₉ × 3869.5

= ^{100 × 3869.5}/₁₀₉

= ³⁸⁶⁹⁵⁰/₁₀₉

= 3550

Thus, Principal = $3550

Thus, the sum borrowed = $3550 Answer

Similar Questions

(1) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 3% simple interest.

(2) Calculate the amount due if Robert borrowed a sum of $3100 at 9% simple interest for 4 years.

(3) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $6216 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 $9384 to clear the loan, then find the time period of the loan.

(5) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $9460 to clear the loan, then find the time period of the loan.

(6) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.

(7) Find the amount to be paid if James borrowed a sum of $5000 at 5% simple interest for 8 years.

(8) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $7661 to clear the loan, then find the time period of the loan.

(9) Find the amount to be paid if Joseph borrowed a sum of $5700 at 6% simple interest for 8 years.

(10) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 2% simple interest.