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

(2) Find the amount to be paid if Mary borrowed a sum of $5050 at 5% simple interest for 8 years.

(3) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 8% simple interest?

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

(5) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $10070 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due if Susan borrowed a sum of $3650 at 7% simple interest for 3 years.

(7) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $7661 to clear the loan, then find the time period of the loan.

(8) In how much time a principal of $3200 will amount to $3712 at a simple interest of 4% per annum?

(9) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 9% simple interest.

(10) Calculate the amount due if Mary borrowed a sum of $3050 at 7% simple interest for 4 years.