Simple Interest
Math MCQs

Question :    William had to pay $3920 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

Correct Answer  $3500

Solution & Explanation

Solution

Given,

Amount (A) = $3920

Rate of Simple Interest (R) = 4%

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

$3920 = P (1 + 4% × 3)

⇒ $3920 = P (1 + ⁴/₁₀₀ × 3)

⇒ $3920 = P (1 + ^{4 × 3}/₁₀₀)

⇒ $3920 = P (1 + ¹²/₁₀₀)

⇒ $3920 = P (^{100 + 12}/₁₀₀)

⇒ $3920 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $3920

⇒ P = ³⁹²⁰/_¹¹²/100

⇒ P = 3920 × ¹⁰⁰/₁₁₂

⇒ P = ^{3920 × 100}/₁₁₂

⇒ P = ³⁹²⁰⁰⁰/₁₁₂

⇒ P = $3500

Thus, the sum borrowed (P) = $3500 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 = 4% per annum

Thus, Interest = 4% of principal

⇒ Interest = 4% of 100 = 4

Thus, Simple Interest for 1 year = 4

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 × 4 = 12

Thus, simple interest for 3 years = 12

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 12 = 112

Calculation of the Principal

Now,

∵ If the Amount is 112, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₂

∴ If the Amount is 3920, then the Principal = ¹⁰⁰/₁₁₂ × 3920

= ^{100 × 3920}/₁₁₂

= ³⁹²⁰⁰⁰/₁₁₂

= 3500

Thus, Principal = $3500

Thus, the sum borrowed = $3500 Answer

Similar Questions

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

(2) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $10332 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due if Michael borrowed a sum of $3300 at 9% simple interest for 4 years.

(4) In how much time a principal of $3100 will amount to $3286 at a simple interest of 3% per annum?

(5) How much loan did Jason borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8855 to clear it?

(6) In how much time a principal of $3000 will amount to $3270 at a simple interest of 3% per annum?

(7) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 8% simple interest.

(8) If Michael paid $3960 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(9) If Sarah paid $4466 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(10) 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.