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) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 4% simple interest?

(2) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $8162 to clear the loan, then find the time period of the loan.

(3) If Elizabeth paid $3864 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(4) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 3% simple interest?

(5) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $6956 to clear the loan, then find the time period of the loan.

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

(7) How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9750 to clear it?

(8) Calculate the amount due if Joseph borrowed a sum of $3700 at 5% simple interest for 4 years.

(9) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 5% simple interest.

(10) Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $9520 to clear the loan, then find the time period of the loan.