Simple Interest
Math MCQs

Question :    Charles had to pay $4485 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

Correct Answer  $3900

Solution & Explanation

Solution

Given,

Amount (A) = $4485

Rate of Simple Interest (R) = 5%

Time (T) = 3 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

$4485 = P (1 + 5% × 3)

⇒ $4485 = P (1 + ⁵/₁₀₀ × 3)

⇒ $4485 = P (1 + ^{5 × 3}/₁₀₀)

⇒ $4485 = P (1 + ¹⁵/₁₀₀)

⇒ $4485 = P (^{100 + 15}/₁₀₀)

⇒ $4485 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $4485

⇒ P = ⁴⁴⁸⁵/_¹¹⁵/100

⇒ P = 4485 × ¹⁰⁰/₁₁₅

⇒ P = ^{4485 × 100}/₁₁₅

⇒ P = ⁴⁴⁸⁵⁰⁰/₁₁₅

⇒ P = $3900

Thus, the sum borrowed (P) = $3900 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 = 3 years

So, we need to calculate the simple interest for the given time period, which is 3 years

Thus, Simple Interest for 3 years = 3 × Simple Interest for 1 year

= 3 × 5 = 15

Thus, simple interest for 3 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 4485, then the Principal = ¹⁰⁰/₁₁₅ × 4485

= ^{100 × 4485}/₁₁₅

= ⁴⁴⁸⁵⁰⁰/₁₁₅

= 3900

Thus, Principal = $3900

Thus, the sum borrowed = $3900 Answer

Similar Questions

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

(2) If Emily paid $5130 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(3) How much loan did Charles borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7080 to clear it?

(4) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 10% simple interest.

(5) Calculate the amount due if Karen borrowed a sum of $3950 at 8% simple interest for 3 years.

(6) Calculate the amount due if William borrowed a sum of $3500 at 10% simple interest for 3 years.

(7) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 3% simple interest.

(8) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $12040 to clear the loan, then find the time period of the loan.

(9) Find the amount to be paid if Jessica borrowed a sum of $5750 at 9% simple interest for 7 years.

(10) If Donald paid $5040 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.