Simple Interest
Math MCQs

Question :    How much loan did Sarah borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7312.5 to clear it?

Correct Answer  $5850

Solution & Explanation

Solution

Given,

Amount (A) = $7312.5

Rate of Simple Interest (R) = 5%

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

$7312.5 = P (1 + 5% × 5)

⇒ $7312.5 = P (1 + ⁵/₁₀₀ × 5)

⇒ $7312.5 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $7312.5 = P (1 + ²⁵/₁₀₀)

⇒ $7312.5 = P (^{100 + 25}/₁₀₀)

⇒ $7312.5 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $7312.5

⇒ P = ^7312.5/_¹²⁵/100

⇒ P = 7312.5 × ¹⁰⁰/₁₂₅

⇒ P = ^{7312.5 × 100}/₁₂₅

⇒ P = ⁷³¹²⁵⁰/₁₂₅

⇒ P = $5850

Thus, the sum borrowed (P) = $5850 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 = 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 × 5 = 25

Thus, simple interest for 5 years = 25

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 25 = 125

Calculation of the Principal

Now,

∵ If the Amount is 125, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₅

∴ If the Amount is 7312.5, then the Principal = ¹⁰⁰/₁₂₅ × 7312.5

= ^{100 × 7312.5}/₁₂₅

= ⁷³¹²⁵⁰/₁₂₅

= 5850

Thus, Principal = $5850

Thus, the sum borrowed = $5850 Answer

Similar Questions

(1) Calculate the amount due if Charles borrowed a sum of $3900 at 8% simple interest for 4 years.

(2) Find the amount to be paid if Charles borrowed a sum of $5900 at 3% simple interest for 7 years.

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

(4) If Paul paid $5452 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(5) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $9176 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due if Richard borrowed a sum of $3600 at 10% simple interest for 4 years.

(7) If Linda paid $3752 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(8) Calculate the amount due if Charles borrowed a sum of $3900 at 9% simple interest for 4 years.

(9) Lisa had to pay $4536 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(10) If Michael borrowed $3300 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.