Simple Interest
Math MCQs

Question :    How much loan did Christopher borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7200 to clear it?

Correct Answer  $6000

Solution & Explanation

Solution

Given,

Amount (A) = $7200

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

$7200 = P (1 + 4% × 5)

⇒ $7200 = P (1 + ⁴/₁₀₀ × 5)

⇒ $7200 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $7200 = P (1 + ²⁰/₁₀₀)

⇒ $7200 = P (^{100 + 20}/₁₀₀)

⇒ $7200 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $7200

⇒ P = ⁷²⁰⁰/_¹²⁰/100

⇒ P = 7200 × ¹⁰⁰/₁₂₀

⇒ P = ^{7200 × 100}/₁₂₀

⇒ P = ⁷²⁰⁰⁰⁰/₁₂₀

⇒ P = $6000

Thus, the sum borrowed (P) = $6000 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 7200, then the Principal = ¹⁰⁰/₁₂₀ × 7200

= ^{100 × 7200}/₁₂₀

= ⁷²⁰⁰⁰⁰/₁₂₀

= 6000

Thus, Principal = $6000

Thus, the sum borrowed = $6000 Answer

Similar Questions

(1) If Ashley paid $5278 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(2) Calculate the amount due if Joseph borrowed a sum of $3700 at 7% simple interest for 4 years.

(3) In how much time a principal of $3100 will amount to $3565 at a simple interest of 5% per annum?

(4) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 10% simple interest?

(5) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 2% simple interest?

(6) If Joshua paid $5880 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(7) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 7% simple interest.

(8) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 10% simple interest.

(9) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 4% simple interest.

(10) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $11560 to clear the loan, then find the time period of the loan.