mcqs Math Simple Interest If Sarah paid $4620 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken. 6926

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Question: ( 1 of 10 ) If Sarah paid $4620 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

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

You selected $3465

Correct Answer $3850

Solution And Explanation

Solution

Given,

Amount (A) = $4620

Rate of Simple Interest (R) = 5%

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

$4620 = P (1 + 5% × 4)

⇒ $4620 = P (1 + ⁵/₁₀₀ × 4)

⇒ $4620 = P (1 + ^{5 × 4}/₁₀₀)

⇒ $4620 = P (1 + ²⁰/₁₀₀)

⇒ $4620 = P (^{100 + 20}/₁₀₀)

⇒ $4620 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $4620

⇒ P = ⁴⁶²⁰/_{¹²⁰/₁₀₀}

⇒ P = 4620 × ¹⁰⁰/₁₂₀

⇒ P = ^{4620 × 100}/₁₂₀

⇒ P = ⁴⁶²⁰⁰⁰/₁₂₀

⇒ P = $3850

Thus, the sum borrowed (P) = $3850 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 = 5% per annum

Thus, Interest = 5% of principal

⇒ Interest = 5% of 100 = 5

Thus, Simple Interest for 1 year = 5

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 × 5 = 20

Thus, simple interest for 4 years = 20

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 20 = 120

Calculation of the Principal

Now,

∵ If the Amount is 120, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₀

∴ If the Amount is 4620, then the Principal = ¹⁰⁰/₁₂₀ × 4620

= ^{100 × 4620}/₁₂₀

= ⁴⁶²⁰⁰⁰/₁₂₀

= 3850

Thus, Principal = $3850

Thus, the sum borrowed = $3850 Answer