Simple Interest
Math MCQs

Question :    If Mark paid $4928 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

Correct Answer  $4400

Solution & Explanation

Solution

Given,

Amount (A) = $4928

Rate of Simple Interest (R) = 3%

Time (T) = 4 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 + 3% × 4)

⇒ $4928 = P (1 + ³/₁₀₀ × 4)

⇒ $4928 = P (1 + ^{3 × 4}/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 = 3% per annum

Thus, Interest = 3% of principal

⇒ Interest = 3% of 100 = 3

Thus, Simple Interest for 1 year = 3

Calculation of the Amount

Since, in the question, time = 4 years

So, we need to calculate the simple interest for the given time period, which is 4 years

Thus, Simple Interest for 4 years = 4 × Simple Interest for 1 year

= 4 × 3 = 12

Thus, simple interest for 4 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) In how much time a principal of $3050 will amount to $3233 at a simple interest of 3% per annum?

(2) Find the amount to be paid if Susan borrowed a sum of $5650 at 10% simple interest for 7 years.

(3) How much loan did Timothy borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8140 to clear it?

(4) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 5% simple interest?

(5) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $8778 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 9% simple interest for 3 years.

(7) How much loan did Sandra borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7095 to clear it?

(8) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 7% simple interest.

(9) Find the amount to be paid if Thomas borrowed a sum of $5800 at 8% simple interest for 8 years.

(10) In how much time a principal of $3000 will amount to $3450 at a simple interest of 5% per annum?