Simple Interest
Math MCQs

Question :    Ashley had to pay $4959.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

Correct Answer  $4550

Solution & Explanation

Solution

Given,

Amount (A) = $4959.5

Rate of Simple Interest (R) = 3%

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

$4959.5 = P (1 + 3% × 3)

⇒ $4959.5 = P (1 + ³/₁₀₀ × 3)

⇒ $4959.5 = P (1 + ^{3 × 3}/₁₀₀)

⇒ $4959.5 = P (1 + ⁹/₁₀₀)

⇒ $4959.5 = P (^{100 + 9}/₁₀₀)

⇒ $4959.5 = P × ¹⁰⁹/₁₀₀

⇒ P × ¹⁰⁹/₁₀₀ = $4959.5

⇒ P = ^4959.5/_¹⁰⁹/100

⇒ P = 4959.5 × ¹⁰⁰/₁₀₉

⇒ P = ^{4959.5 × 100}/₁₀₉

⇒ P = ⁴⁹⁵⁹⁵⁰/₁₀₉

⇒ P = $4550

Thus, the sum borrowed (P) = $4550 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 = 3% per annum

Thus, Interest = 3% of principal

⇒ Interest = 3% of 100 = 3

Thus, Simple Interest for 1 year = 3

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 × 3 = 9

Thus, simple interest for 3 years = 9

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 9 = 109

Calculation of the Principal

Now,

∵ If the Amount is 109, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₀₉

∴ If the Amount is 4959.5, then the Principal = ¹⁰⁰/₁₀₉ × 4959.5

= ^{100 × 4959.5}/₁₀₉

= ⁴⁹⁵⁹⁵⁰/₁₀₉

= 4550

Thus, Principal = $4550

Thus, the sum borrowed = $4550 Answer

Similar Questions

(1) Calculate the amount due if Karen borrowed a sum of $3950 at 7% simple interest for 4 years.

(2) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 9% simple interest.

(3) If Daniel paid $4592 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(4) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $9676 to clear the loan, then find the time period of the loan.

(5) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $8360 to clear the loan, then find the time period of the loan.

(6) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $11340 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due if Thomas borrowed a sum of $3800 at 3% simple interest for 4 years.

(8) If Michael paid $3696 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(9) Find the amount to be paid if Robert borrowed a sum of $5100 at 3% simple interest for 7 years.

(10) Find the amount to be paid if Joseph borrowed a sum of $5700 at 5% simple interest for 7 years.