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) Michelle had to pay $5247 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(2) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 9% simple interest.

(3) If Betty paid $5100 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(4) Find the amount to be paid if Barbara borrowed a sum of $5550 at 8% simple interest for 8 years.

(5) Find the amount to be paid if Sarah borrowed a sum of $5850 at 4% simple interest for 8 years.

(6) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 3% simple interest.

(7) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $8008 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due if Christopher borrowed a sum of $4000 at 3% simple interest for 3 years.

(9) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $10608 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due if Karen borrowed a sum of $3950 at 8% simple interest for 3 years.