Simple Interest
Math MCQs

Question :    How much loan did Ronald borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9000 to clear it?

Correct Answer  $7500

Solution & Explanation

Solution

Given,

Amount (A) = $9000

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

$9000 = P (1 + 4% × 5)

⇒ $9000 = P (1 + ⁴/₁₀₀ × 5)

⇒ $9000 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $9000 = P (1 + ²⁰/₁₀₀)

⇒ $9000 = P (^{100 + 20}/₁₀₀)

⇒ $9000 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $9000

⇒ P = ⁹⁰⁰⁰/_¹²⁰/100

⇒ P = 9000 × ¹⁰⁰/₁₂₀

⇒ P = ^{9000 × 100}/₁₂₀

⇒ P = ⁹⁰⁰⁰⁰⁰/₁₂₀

⇒ P = $7500

Thus, the sum borrowed (P) = $7500 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 9000, then the Principal = ¹⁰⁰/₁₂₀ × 9000

= ^{100 × 9000}/₁₂₀

= ⁹⁰⁰⁰⁰⁰/₁₂₀

= 7500

Thus, Principal = $7500

Thus, the sum borrowed = $7500 Answer

Similar Questions

(1) If Michelle paid $5940 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(2) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $7140 to clear the loan, then find the time period of the loan.

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

(4) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $8804 to clear the loan, then find the time period of the loan.

(5) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $11210 to clear the loan, then find the time period of the loan.

(6) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $11400 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due if James borrowed a sum of $3000 at 5% simple interest for 3 years.

(8) 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.

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

(10) Find the amount to be paid if Joseph borrowed a sum of $5700 at 5% simple interest for 8 years.