Simple Interest
Math MCQs

Question :    Karen had to pay $4542.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

Correct Answer  $3950

Solution & Explanation

Solution

Given,

Amount (A) = $4542.5

Rate of Simple Interest (R) = 5%

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

$4542.5 = P (1 + 5% × 3)

⇒ $4542.5 = P (1 + ⁵/₁₀₀ × 3)

⇒ $4542.5 = P (1 + ^{5 × 3}/₁₀₀)

⇒ $4542.5 = P (1 + ¹⁵/₁₀₀)

⇒ $4542.5 = P (^{100 + 15}/₁₀₀)

⇒ $4542.5 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $4542.5

⇒ P = ^4542.5/_¹¹⁵/100

⇒ P = 4542.5 × ¹⁰⁰/₁₁₅

⇒ P = ^{4542.5 × 100}/₁₁₅

⇒ P = ⁴⁵⁴²⁵⁰/₁₁₅

⇒ P = $3950

Thus, the sum borrowed (P) = $3950 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 = 5% per annum

Thus, Interest = 5% of principal

⇒ Interest = 5% of 100 = 5

Thus, Simple Interest for 1 year = 5

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 × 5 = 15

Thus, simple interest for 3 years = 15

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 15 = 115

Calculation of the Principal

Now,

∵ If the Amount is 115, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₅

∴ If the Amount is 4542.5, then the Principal = ¹⁰⁰/₁₁₅ × 4542.5

= ^{100 × 4542.5}/₁₁₅

= ⁴⁵⁴²⁵⁰/₁₁₅

= 3950

Thus, Principal = $3950

Thus, the sum borrowed = $3950 Answer

Similar Questions

(1) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 7% simple interest?

(2) Calculate the amount due if Patricia borrowed a sum of $3150 at 6% simple interest for 3 years.

(3) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $6512 to clear the loan, then find the time period of the loan.

(4) If Joseph paid $4440 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(5) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 9% simple interest?

(6) What amount will be due after 2 years if John borrowed a sum of $3100 at a 4% simple interest?

(7) Find the amount to be paid if Christopher borrowed a sum of $6000 at 8% simple interest for 7 years.

(8) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 3% simple interest.

(9) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 4% simple interest.

(10) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $5822 to clear the loan, then find the time period of the loan.