Simple Interest
MCQs Math

Question:   ( 2 of 10 )  How much loan did Sharon borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8525 to clear it?

You selected   $6393.75

Correct Answer  $7750

Solution And Explanation

Solution

Given,

Amount (A) = $8525

Rate of Simple Interest (R) = 2%

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

$8525 = P (1 + 2% × 5)

⇒ $8525 = P (1 + ²/₁₀₀ × 5)

⇒ $8525 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $8525 = P (1 + ¹⁰/₁₀₀)

⇒ $8525 = P (^{100 + 10}/₁₀₀)

⇒ $8525 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $8525

⇒ P = ⁸⁵²⁵/_¹¹⁰/100

⇒ P = 8525 × ¹⁰⁰/₁₁₀

⇒ P = ^{8525 × 100}/₁₁₀

⇒ P = ⁸⁵²⁵⁰⁰/₁₁₀

⇒ P = $7750

Thus, the sum borrowed (P) = $7750 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 = 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 × 2 = 10

Thus, simple interest for 5 years = 10

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 10 = 110

Calculation of the Principal

Now,

∵ If the Amount is 110, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₀

∴ If the Amount is 8525, then the Principal = ¹⁰⁰/₁₁₀ × 8525

= ^{100 × 8525}/₁₁₀

= ⁸⁵²⁵⁰⁰/₁₁₀

= 7750

Thus, Principal = $7750

Thus, the sum borrowed = $7750 Answer