Simple Interest
Math MCQs

Question :    Patricia had to pay $3433.5 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  $3150

Solution & Explanation

Solution

Given,

Amount (A) = $3433.5

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

$3433.5 = P (1 + 3% × 3)

⇒ $3433.5 = P (1 + ³/₁₀₀ × 3)

⇒ $3433.5 = P (1 + ^{3 × 3}/₁₀₀)

⇒ $3433.5 = P (1 + ⁹/₁₀₀)

⇒ $3433.5 = P (^{100 + 9}/₁₀₀)

⇒ $3433.5 = P × ¹⁰⁹/₁₀₀

⇒ P × ¹⁰⁹/₁₀₀ = $3433.5

⇒ P = ^3433.5/_¹⁰⁹/100

⇒ P = 3433.5 × ¹⁰⁰/₁₀₉

⇒ P = ^{3433.5 × 100}/₁₀₉

⇒ P = ³⁴³³⁵⁰/₁₀₉

⇒ P = $3150

Thus, the sum borrowed (P) = $3150 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 3433.5, then the Principal = ¹⁰⁰/₁₀₉ × 3433.5

= ^{100 × 3433.5}/₁₀₉

= ³⁴³³⁵⁰/₁₀₉

= 3150

Thus, Principal = $3150

Thus, the sum borrowed = $3150 Answer

Similar Questions

(1) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 6% simple interest.

(2) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 4% simple interest?

(3) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 10% simple interest.

(4) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $11868 to clear the loan, then find the time period of the loan.

(5) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $10800 to clear the loan, then find the time period of the loan.

(6) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $9548 to clear the loan, then find the time period of the loan.

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

(8) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 3% simple interest.

(9) How much loan did Michael borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6625 to clear it?

(10) Calculate the amount due if Robert borrowed a sum of $3100 at 7% simple interest for 3 years.