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 Sarah borrowed $3850 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(2) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $7400 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 7% simple interest.

(4) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 4% simple interest.

(5) If Lisa paid $4374 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(6) In how much time a principal of $3050 will amount to $3294 at a simple interest of 4% per annum?

(7) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 2% simple interest.

(8) Find the amount to be paid if Barbara borrowed a sum of $5550 at 5% simple interest for 8 years.

(9) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 2% simple interest for 3 years.

(10) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $9768 to clear the loan, then find the time period of the loan.