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) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 3% simple interest?

(2) Paul had to pay $4982 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(3) Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $8584 to clear the loan, then find the time period of the loan.

(4) How much loan did Emily borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7425 to clear it?

(5) How much loan did Laura borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9027.5 to clear it?

(6) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $8791 to clear the loan, then find the time period of the loan.

(7) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $9720 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 6% simple interest.

(9) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 4% simple interest?

(10) Calculate the amount due if Richard borrowed a sum of $3600 at 3% simple interest for 4 years.