Simple Interest
Math MCQs

Question :    Donna had to pay $5286.5 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  $4850

Solution & Explanation

Solution

Given,

Amount (A) = $5286.5

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

$5286.5 = P (1 + 3% × 3)

⇒ $5286.5 = P (1 + ³/₁₀₀ × 3)

⇒ $5286.5 = P (1 + ^{3 × 3}/₁₀₀)

⇒ $5286.5 = P (1 + ⁹/₁₀₀)

⇒ $5286.5 = P (^{100 + 9}/₁₀₀)

⇒ $5286.5 = P × ¹⁰⁹/₁₀₀

⇒ P × ¹⁰⁹/₁₀₀ = $5286.5

⇒ P = ^5286.5/_¹⁰⁹/100

⇒ P = 5286.5 × ¹⁰⁰/₁₀₉

⇒ P = ^{5286.5 × 100}/₁₀₉

⇒ P = ⁵²⁸⁶⁵⁰/₁₀₉

⇒ P = $4850

Thus, the sum borrowed (P) = $4850 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 5286.5, then the Principal = ¹⁰⁰/₁₀₉ × 5286.5

= ^{100 × 5286.5}/₁₀₉

= ⁵²⁸⁶⁵⁰/₁₀₉

= 4850

Thus, Principal = $4850

Thus, the sum borrowed = $4850 Answer

Similar Questions

(1) Find the amount to be paid if William borrowed a sum of $5500 at 5% simple interest for 7 years.

(2) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 4% simple interest.

(3) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $8313 to clear the loan, then find the time period of the loan.

(4) If Kimberly paid $5022 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(5) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $6528 to clear the loan, then find the time period of the loan.

(6) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $6936 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 8% simple interest.

(8) Robert took a loan of $4200 at the rate of 7% simple interest per annum. If he paid an amount of $6846 to clear the loan, then find the time period of the loan.

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

(10) Calculate the amount due if Sarah borrowed a sum of $3850 at 10% simple interest for 4 years.