Simple Interest
Math MCQs

Question :    How much loan did Matthew borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7130 to clear it?

Correct Answer  $6200

Solution & Explanation

Solution

Given,

Amount (A) = $7130

Rate of Simple Interest (R) = 3%

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

$7130 = P (1 + 3% × 5)

⇒ $7130 = P (1 + ³/₁₀₀ × 5)

⇒ $7130 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $7130 = P (1 + ¹⁵/₁₀₀)

⇒ $7130 = P (^{100 + 15}/₁₀₀)

⇒ $7130 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $7130

⇒ P = ⁷¹³⁰/_¹¹⁵/100

⇒ P = 7130 × ¹⁰⁰/₁₁₅

⇒ P = ^{7130 × 100}/₁₁₅

⇒ P = ⁷¹³⁰⁰⁰/₁₁₅

⇒ P = $6200

Thus, the sum borrowed (P) = $6200 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 = 3% per annum

Thus, Interest = 3% of principal

⇒ Interest = 3% of 100 = 3

Thus, Simple Interest for 1 year = 3

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 × 3 = 15

Thus, simple interest for 5 years = 15

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 15 = 115

Calculation of the Principal

Now,

∵ If the Amount is 115, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₅

∴ If the Amount is 7130, then the Principal = ¹⁰⁰/₁₁₅ × 7130

= ^{100 × 7130}/₁₁₅

= ⁷¹³⁰⁰⁰/₁₁₅

= 6200

Thus, Principal = $6200

Thus, the sum borrowed = $6200 Answer

Similar Questions

(1) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $10000 to clear the loan, then find the time period of the loan.

(2) If Sarah paid $4158 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(3) Find the amount to be paid if William borrowed a sum of $5500 at 3% simple interest for 7 years.

(4) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 4% simple interest?

(5) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $8692 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 $9943 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 2% simple interest.

(8) Calculate the amount due if Michael borrowed a sum of $3300 at 10% simple interest for 4 years.

(9) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $8580 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due if James borrowed a sum of $3000 at 10% simple interest for 4 years.