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) Jennifer had to pay $3737.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(2) 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.

(3) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 9% simple interest.

(4) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 8% simple interest?

(5) Find the amount to be paid if Mary borrowed a sum of $5050 at 2% simple interest for 7 years.

(6) Karen had to pay $4424 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(7) Jennifer took a loan of $4500 at the rate of 10% simple interest per annum. If he paid an amount of $8100 to clear the loan, then find the time period of the loan.

(8) In how much time a principal of $3100 will amount to $3348 at a simple interest of 2% per annum?

(9) Find the amount to be paid if John borrowed a sum of $5200 at 8% simple interest for 8 years.

(10) Find the amount to be paid if David borrowed a sum of $5400 at 6% simple interest for 7 years.