Simple Interest
Math MCQs

Question :    How much loan did Margaret borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7302.5 to clear it?

Correct Answer  $6350

Solution & Explanation

Solution

Given,

Amount (A) = $7302.5

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

$7302.5 = P (1 + 3% × 5)

⇒ $7302.5 = P (1 + ³/₁₀₀ × 5)

⇒ $7302.5 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $7302.5 = P (1 + ¹⁵/₁₀₀)

⇒ $7302.5 = P (^{100 + 15}/₁₀₀)

⇒ $7302.5 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $7302.5

⇒ P = ^7302.5/_¹¹⁵/100

⇒ P = 7302.5 × ¹⁰⁰/₁₁₅

⇒ P = ^{7302.5 × 100}/₁₁₅

⇒ P = ⁷³⁰²⁵⁰/₁₁₅

⇒ P = $6350

Thus, the sum borrowed (P) = $6350 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 7302.5, then the Principal = ¹⁰⁰/₁₁₅ × 7302.5

= ^{100 × 7302.5}/₁₁₅

= ⁷³⁰²⁵⁰/₁₁₅

= 6350

Thus, Principal = $6350

Thus, the sum borrowed = $6350 Answer

Similar Questions

(1) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 2% simple interest.

(2) How much loan did Mary borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5555 to clear it?

(3) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $9780 to clear the loan, then find the time period of the loan.

(4) Find the amount to be paid if John borrowed a sum of $5200 at 9% simple interest for 8 years.

(5) Calculate the amount due if Joseph borrowed a sum of $3700 at 6% simple interest for 4 years.

(6) How much loan did Michael borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6360 to clear it?

(7) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $11390 to clear the loan, then find the time period of the loan.

(8) 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.

(9) Calculate the amount due if Thomas borrowed a sum of $3800 at 2% simple interest for 3 years.

(10) If Jennifer paid $3770 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.