Simple Interest
Math MCQs

Question :    Mark had to pay $4928 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  $4400

Solution & Explanation

Solution

Given,

Amount (A) = $4928

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

$4928 = P (1 + 4% × 3)

⇒ $4928 = P (1 + ⁴/₁₀₀ × 3)

⇒ $4928 = P (1 + ^{4 × 3}/₁₀₀)

⇒ $4928 = P (1 + ¹²/₁₀₀)

⇒ $4928 = P (^{100 + 12}/₁₀₀)

⇒ $4928 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $4928

⇒ P = ⁴⁹²⁸/_¹¹²/100

⇒ P = 4928 × ¹⁰⁰/₁₁₂

⇒ P = ^{4928 × 100}/₁₁₂

⇒ P = ⁴⁹²⁸⁰⁰/₁₁₂

⇒ P = $4400

Thus, the sum borrowed (P) = $4400 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 4928, then the Principal = ¹⁰⁰/₁₁₂ × 4928

= ^{100 × 4928}/₁₁₂

= ⁴⁹²⁸⁰⁰/₁₁₂

= 4400

Thus, Principal = $4400

Thus, the sum borrowed = $4400 Answer

Similar Questions

(1) If William paid $3920 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(2) How much loan did James borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6000 to clear it?

(3) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 9% simple interest.

(4) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 7% simple interest.

(5) Calculate the amount due if Patricia borrowed a sum of $3150 at 5% simple interest for 4 years.

(6) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $6240 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due if Barbara borrowed a sum of $3550 at 10% simple interest for 3 years.

(8) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $9472 to clear the loan, then find the time period of the loan.

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

(10) How much loan did Betty borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6875 to clear it?