Simple Interest
Math MCQs

Question :    Emily had to pay $5177.5 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  $4750

Solution & Explanation

Solution

Given,

Amount (A) = $5177.5

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

$5177.5 = P (1 + 3% × 3)

⇒ $5177.5 = P (1 + ³/₁₀₀ × 3)

⇒ $5177.5 = P (1 + ^{3 × 3}/₁₀₀)

⇒ $5177.5 = P (1 + ⁹/₁₀₀)

⇒ $5177.5 = P (^{100 + 9}/₁₀₀)

⇒ $5177.5 = P × ¹⁰⁹/₁₀₀

⇒ P × ¹⁰⁹/₁₀₀ = $5177.5

⇒ P = ^5177.5/_¹⁰⁹/100

⇒ P = 5177.5 × ¹⁰⁰/₁₀₉

⇒ P = ^{5177.5 × 100}/₁₀₉

⇒ P = ⁵¹⁷⁷⁵⁰/₁₀₉

⇒ P = $4750

Thus, the sum borrowed (P) = $4750 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 5177.5, then the Principal = ¹⁰⁰/₁₀₉ × 5177.5

= ^{100 × 5177.5}/₁₀₉

= ⁵¹⁷⁷⁵⁰/₁₀₉

= 4750

Thus, Principal = $4750

Thus, the sum borrowed = $4750 Answer

Similar Questions

(1) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 6% simple interest.

(2) Find the amount to be paid if Sarah borrowed a sum of $5850 at 6% simple interest for 8 years.

(3) Calculate the amount due if John borrowed a sum of $3200 at 5% simple interest for 3 years.

(4) Calculate the amount due if Sarah borrowed a sum of $3850 at 3% simple interest for 4 years.

(5) In how much time a principal of $3100 will amount to $3565 at a simple interest of 3% per annum?

(6) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $9324 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 3% simple interest.

(8) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $9804 to clear the loan, then find the time period of the loan.

(9) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $7380 to clear the loan, then find the time period of the loan.

(10) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $7920 to clear the loan, then find the time period of the loan.