Simple Interest
Math MCQs

Question :    Sarah had to pay $4427.5 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  $3850

Solution & Explanation

Solution

Given,

Amount (A) = $4427.5

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

$4427.5 = P (1 + 5% × 3)

⇒ $4427.5 = P (1 + ⁵/₁₀₀ × 3)

⇒ $4427.5 = P (1 + ^{5 × 3}/₁₀₀)

⇒ $4427.5 = P (1 + ¹⁵/₁₀₀)

⇒ $4427.5 = P (^{100 + 15}/₁₀₀)

⇒ $4427.5 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $4427.5

⇒ P = ^4427.5/_¹¹⁵/100

⇒ P = 4427.5 × ¹⁰⁰/₁₁₅

⇒ P = ^{4427.5 × 100}/₁₁₅

⇒ P = ⁴⁴²⁷⁵⁰/₁₁₅

⇒ 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 = 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 4427.5, then the Principal = ¹⁰⁰/₁₁₅ × 4427.5

= ^{100 × 4427.5}/₁₁₅

= ⁴⁴²⁷⁵⁰/₁₁₅

= 3850

Thus, Principal = $3850

Thus, the sum borrowed = $3850 Answer

Similar Questions

(1) How much loan did Patricia borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5665 to clear it?

(2) Find the amount to be paid if Thomas borrowed a sum of $5800 at 6% simple interest for 8 years.

(3) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $8840 to clear the loan, then find the time period of the loan.

(4) If Paul paid $5076 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(5) Calculate the amount due if David borrowed a sum of $3400 at 5% simple interest for 4 years.

(6) Calculate the amount due if James borrowed a sum of $3000 at 6% simple interest for 4 years.

(7) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $8802 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 2% simple interest.

(9) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 5% simple interest.

(10) Calculate the amount due if Patricia borrowed a sum of $3150 at 6% simple interest for 3 years.