Simple Interest
Math MCQs

Question :    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.

Correct Answer  $3950

Solution & Explanation

Solution

Given,

Amount (A) = $4424

Rate of Simple Interest (R) = 4%

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

$4424 = P (1 + 4% × 3)

⇒ $4424 = P (1 + ⁴/₁₀₀ × 3)

⇒ $4424 = P (1 + ^{4 × 3}/₁₀₀)

⇒ $4424 = P (1 + ¹²/₁₀₀)

⇒ $4424 = P (^{100 + 12}/₁₀₀)

⇒ $4424 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $4424

⇒ P = ⁴⁴²⁴/_¹¹²/100

⇒ P = 4424 × ¹⁰⁰/₁₁₂

⇒ P = ^{4424 × 100}/₁₁₂

⇒ P = ⁴⁴²⁴⁰⁰/₁₁₂

⇒ 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 = 4% per annum

Thus, Interest = 4% of principal

⇒ Interest = 4% of 100 = 4

Thus, Simple Interest for 1 year = 4

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 × 4 = 12

Thus, simple interest for 3 years = 12

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 12 = 112

Calculation of the Principal

Now,

∵ If the Amount is 112, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₂

∴ If the Amount is 4424, then the Principal = ¹⁰⁰/₁₁₂ × 4424

= ^{100 × 4424}/₁₁₂

= ⁴⁴²⁴⁰⁰/₁₁₂

= 3950

Thus, Principal = $3950

Thus, the sum borrowed = $3950 Answer

Similar Questions

(1) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 4% simple interest.

(2) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $6364 to clear the loan, then find the time period of the loan.

(3) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $11400 to clear the loan, then find the time period of the loan.

(4) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $8520 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 4% simple interest.

(6) Find the amount to be paid if James borrowed a sum of $5000 at 5% simple interest for 7 years.

(7) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 6% simple interest?

(8) Find the amount to be paid if James borrowed a sum of $5000 at 7% simple interest for 8 years.

(9) Calculate the amount due if Barbara borrowed a sum of $3550 at 3% simple interest for 3 years.

(10) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $7992 to clear the loan, then find the time period of the loan.