Simple Interest
Math MCQs

Question :    If Mary paid $3294 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

Correct Answer  $3050

Solution & Explanation

Solution

Given,

Amount (A) = $3294

Rate of Simple Interest (R) = 2%

Time (T) = 4 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

$3294 = P (1 + 2% × 4)

⇒ $3294 = P (1 + ²/₁₀₀ × 4)

⇒ $3294 = P (1 + ^{2 × 4}/₁₀₀)

⇒ $3294 = P (1 + ⁸/₁₀₀)

⇒ $3294 = P (^{100 + 8}/₁₀₀)

⇒ $3294 = P × ¹⁰⁸/₁₀₀

⇒ P × ¹⁰⁸/₁₀₀ = $3294

⇒ P = ³²⁹⁴/_¹⁰⁸/100

⇒ P = 3294 × ¹⁰⁰/₁₀₈

⇒ P = ^{3294 × 100}/₁₀₈

⇒ P = ³²⁹⁴⁰⁰/₁₀₈

⇒ P = $3050

Thus, the sum borrowed (P) = $3050 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 = 2% per annum

Thus, Interest = 2% of principal

⇒ Interest = 2% of 100 = 2

Thus, Simple Interest for 1 year = 2

Calculation of the Amount

Since, in the question, time = 4 years

So, we need to calculate the simple interest for the given time period, which is 4 years

Thus, Simple Interest for 4 years = 4 × Simple Interest for 1 year

= 4 × 2 = 8

Thus, simple interest for 4 years = 8

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 8 = 108

Calculation of the Principal

Now,

∵ If the Amount is 108, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₀₈

∴ If the Amount is 3294, then the Principal = ¹⁰⁰/₁₀₈ × 3294

= ^{100 × 3294}/₁₀₈

= ³²⁹⁴⁰⁰/₁₀₈

= 3050

Thus, Principal = $3050

Thus, the sum borrowed = $3050 Answer

Similar Questions

(1) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 8% simple interest?

(2) Find the amount to be paid if Michael borrowed a sum of $5300 at 6% simple interest for 7 years.

(3) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 4% simple interest.

(4) How much loan did Paul borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7370 to clear it?

(5) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $7912 to clear the loan, then find the time period of the loan.

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

(7) Find the amount to be paid if Charles borrowed a sum of $5900 at 7% simple interest for 8 years.

(8) Calculate the amount due if John borrowed a sum of $3200 at 6% simple interest for 4 years.

(9) If Elizabeth borrowed $3450 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(10) How much loan did Mark borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7680 to clear it?