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) How much loan did Robert borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5865 to clear it?

(2) Calculate the amount due if David borrowed a sum of $3400 at 9% simple interest for 3 years.

(3) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 4% simple interest?

(4) How much loan did Nancy borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6765 to clear it?

(5) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $10318 to clear the loan, then find the time period of the loan.

(6) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $11590 to clear the loan, then find the time period of the loan.

(7) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 8% simple interest?

(8) In how much time a principal of $3200 will amount to $3456 at a simple interest of 2% per annum?

(9) Calculate the amount due if Jennifer borrowed a sum of $3250 at 9% simple interest for 3 years.

(10) If Mark paid $4928 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.