Simple Interest
Math MCQs

Question :    John had to pay $3488 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  $3200

Solution & Explanation

Solution

Given,

Amount (A) = $3488

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

$3488 = P (1 + 3% × 3)

⇒ $3488 = P (1 + ³/₁₀₀ × 3)

⇒ $3488 = P (1 + ^{3 × 3}/₁₀₀)

⇒ $3488 = P (1 + ⁹/₁₀₀)

⇒ $3488 = P (^{100 + 9}/₁₀₀)

⇒ $3488 = P × ¹⁰⁹/₁₀₀

⇒ P × ¹⁰⁹/₁₀₀ = $3488

⇒ P = ³⁴⁸⁸/_¹⁰⁹/100

⇒ P = 3488 × ¹⁰⁰/₁₀₉

⇒ P = ^{3488 × 100}/₁₀₉

⇒ P = ³⁴⁸⁸⁰⁰/₁₀₉

⇒ P = $3200

Thus, the sum borrowed (P) = $3200 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 3488, then the Principal = ¹⁰⁰/₁₀₉ × 3488

= ^{100 × 3488}/₁₀₉

= ³⁴⁸⁸⁰⁰/₁₀₉

= 3200

Thus, Principal = $3200

Thus, the sum borrowed = $3200 Answer

Similar Questions

(1) Joshua had to pay $5194 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(2) Calculate the amount due if William borrowed a sum of $3500 at 10% simple interest for 3 years.

(3) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $11730 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 3% simple interest.

(5) In how much time a principal of $3050 will amount to $3660 at a simple interest of 4% per annum?

(6) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 5% simple interest?

(7) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $9231 to clear the loan, then find the time period of the loan.

(8) If Joshua paid $5684 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(9) If Joseph paid $4292 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(10) Calculate the amount due if Joseph borrowed a sum of $3700 at 6% simple interest for 4 years.