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) Calculate the amount due if John borrowed a sum of $3200 at 10% simple interest for 3 years.

(2) In how much time a principal of $3000 will amount to $3480 at a simple interest of 4% per annum?

(3) Calculate the amount due if William borrowed a sum of $3500 at 7% simple interest for 4 years.

(4) Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $8162 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 10% simple interest.

(6) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 2% simple interest?

(7) If Susan paid $3942 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(8) What amount does William have to pay after 6 years if he takes a loan of $3500 at 4% simple interest?

(9) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 5% simple interest?

(10) Calculate the amount due if William borrowed a sum of $3500 at 4% simple interest for 4 years.