mcqs Math Simple Interest If David paid $3672 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken. 6794

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Question: ( 1 of 10 ) If David paid $3672 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(A)  $6750
(B)  $5400
(C)  $8100
(D)  $8424

You selected $2754

Correct Answer $3400

Solution And Explanation

Solution

Given,

Amount (A) = $3672

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

$3672 = P (1 + 2% × 4)

⇒ $3672 = P (1 + ²/₁₀₀ × 4)

⇒ $3672 = P (1 + ^{2 × 4}/₁₀₀)

⇒ $3672 = P (1 + ⁸/₁₀₀)

⇒ $3672 = P (^{100 + 8}/₁₀₀)

⇒ $3672 = P × ¹⁰⁸/₁₀₀

⇒ P × ¹⁰⁸/₁₀₀ = $3672

⇒ P = ³⁶⁷²/_{¹⁰⁸/₁₀₀}

⇒ P = 3672 × ¹⁰⁰/₁₀₈

⇒ P = ^{3672 × 100}/₁₀₈

⇒ P = ³⁶⁷²⁰⁰/₁₀₈

⇒ P = $3400

Thus, the sum borrowed (P) = $3400 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 3672, then the Principal = ¹⁰⁰/₁₀₈ × 3672

= ^{100 × 3672}/₁₀₈

= ³⁶⁷²⁰⁰/₁₀₈

= 3400

Thus, Principal = $3400

Thus, the sum borrowed = $3400 Answer