Simple Interest
Math MCQs

Question :    Robert had to pay $3379 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  $3100

Solution & Explanation

Solution

Given,

Amount (A) = $3379

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

$3379 = P (1 + 3% × 3)

⇒ $3379 = P (1 + ³/₁₀₀ × 3)

⇒ $3379 = P (1 + ^{3 × 3}/₁₀₀)

⇒ $3379 = P (1 + ⁹/₁₀₀)

⇒ $3379 = P (^{100 + 9}/₁₀₀)

⇒ $3379 = P × ¹⁰⁹/₁₀₀

⇒ P × ¹⁰⁹/₁₀₀ = $3379

⇒ P = ³³⁷⁹/_¹⁰⁹/100

⇒ P = 3379 × ¹⁰⁰/₁₀₉

⇒ P = ^{3379 × 100}/₁₀₉

⇒ P = ³³⁷⁹⁰⁰/₁₀₉

⇒ P = $3100

Thus, the sum borrowed (P) = $3100 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 3379, then the Principal = ¹⁰⁰/₁₀₉ × 3379

= ^{100 × 3379}/₁₀₉

= ³³⁷⁹⁰⁰/₁₀₉

= 3100

Thus, Principal = $3100

Thus, the sum borrowed = $3100 Answer

Similar Questions

(1) Calculate the amount due if Mary borrowed a sum of $3050 at 2% simple interest for 4 years.

(2) Calculate the amount due if Sarah borrowed a sum of $3850 at 3% simple interest for 3 years.

(3) If William borrowed $3500 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(4) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 2% simple interest.

(5) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 7% simple interest.

(6) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 8% simple interest?

(7) If Linda paid $3886 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(8) If Daniel paid $4756 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(9) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $10200 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 9% simple interest for 7 years.