Simple Interest
Math MCQs

Question :    Sarah had to pay $4196.5 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  $3850

Solution & Explanation

Solution

Given,

Amount (A) = $4196.5

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

$4196.5 = P (1 + 3% × 3)

⇒ $4196.5 = P (1 + ³/₁₀₀ × 3)

⇒ $4196.5 = P (1 + ^{3 × 3}/₁₀₀)

⇒ $4196.5 = P (1 + ⁹/₁₀₀)

⇒ $4196.5 = P (^{100 + 9}/₁₀₀)

⇒ $4196.5 = P × ¹⁰⁹/₁₀₀

⇒ P × ¹⁰⁹/₁₀₀ = $4196.5

⇒ P = ^4196.5/_¹⁰⁹/100

⇒ P = 4196.5 × ¹⁰⁰/₁₀₉

⇒ P = ^{4196.5 × 100}/₁₀₉

⇒ P = ⁴¹⁹⁶⁵⁰/₁₀₉

⇒ 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 = 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 4196.5, then the Principal = ¹⁰⁰/₁₀₉ × 4196.5

= ^{100 × 4196.5}/₁₀₉

= ⁴¹⁹⁶⁵⁰/₁₀₉

= 3850

Thus, Principal = $3850

Thus, the sum borrowed = $3850 Answer

Similar Questions

(1) If Ashley paid $4914 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(2) Find the amount to be paid if Joseph borrowed a sum of $5700 at 2% simple interest for 8 years.

(3) Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $6956 to clear the loan, then find the time period of the loan.

(4) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $9672 to clear the loan, then find the time period of the loan.

(5) Find the amount to be paid if Thomas borrowed a sum of $5800 at 8% simple interest for 7 years.

(6) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $6314 to clear the loan, then find the time period of the loan.

(7) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $9540 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due if Thomas borrowed a sum of $3800 at 2% simple interest for 3 years.

(9) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $10626 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 6% simple interest.