Simple Interest
Math MCQs

Question :    How much loan did George borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8760 to clear it?

Correct Answer  $7300

Solution & Explanation

Solution

Given,

Amount (A) = $8760

Rate of Simple Interest (R) = 4%

Time (T) = 5 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

$8760 = P (1 + 4% × 5)

⇒ $8760 = P (1 + ⁴/₁₀₀ × 5)

⇒ $8760 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $8760 = P (1 + ²⁰/₁₀₀)

⇒ $8760 = P (^{100 + 20}/₁₀₀)

⇒ $8760 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $8760

⇒ P = ⁸⁷⁶⁰/_¹²⁰/100

⇒ P = 8760 × ¹⁰⁰/₁₂₀

⇒ P = ^{8760 × 100}/₁₂₀

⇒ P = ⁸⁷⁶⁰⁰⁰/₁₂₀

⇒ P = $7300

Thus, the sum borrowed (P) = $7300 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 = 5 years

So, we need to calculate the simple interest for the given time period, which is 5 years

Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year

= 5 × 4 = 20

Thus, simple interest for 5 years = 20

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 20 = 120

Calculation of the Principal

Now,

∵ If the Amount is 120, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₀

∴ If the Amount is 8760, then the Principal = ¹⁰⁰/₁₂₀ × 8760

= ^{100 × 8760}/₁₂₀

= ⁸⁷⁶⁰⁰⁰/₁₂₀

= 7300

Thus, Principal = $7300

Thus, the sum borrowed = $7300 Answer

Similar Questions

(1) If Kenneth paid $5400 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(2) Calculate the amount due if Michael borrowed a sum of $3300 at 7% simple interest for 3 years.

(3) If Jessica paid $4200 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(4) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 4% simple interest for 3 years.

(5) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 9% simple interest.

(6) Calculate the amount due if William borrowed a sum of $3500 at 7% simple interest for 4 years.

(7) Calculate the amount due if John borrowed a sum of $3200 at 7% simple interest for 4 years.

(8) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $11160 to clear the loan, then find the time period of the loan.

(9) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $6956 to clear the loan, then find the time period of the loan.

(10) John had to pay $3392 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.