Simple Interest
Math MCQs

Question :    If Michael paid $3828 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

Correct Answer  $3300

Solution & Explanation

Solution

Given,

Amount (A) = $3828

Rate of Simple Interest (R) = 4%

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

$3828 = P (1 + 4% × 4)

⇒ $3828 = P (1 + ⁴/₁₀₀ × 4)

⇒ $3828 = P (1 + ^{4 × 4}/₁₀₀)

⇒ $3828 = P (1 + ¹⁶/₁₀₀)

⇒ $3828 = P (^{100 + 16}/₁₀₀)

⇒ $3828 = P × ¹¹⁶/₁₀₀

⇒ P × ¹¹⁶/₁₀₀ = $3828

⇒ P = ³⁸²⁸/_¹¹⁶/100

⇒ P = 3828 × ¹⁰⁰/₁₁₆

⇒ P = ^{3828 × 100}/₁₁₆

⇒ P = ³⁸²⁸⁰⁰/₁₁₆

⇒ P = $3300

Thus, the sum borrowed (P) = $3300 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 = 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 × 4 = 16

Thus, simple interest for 4 years = 16

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 16 = 116

Calculation of the Principal

Now,

∵ If the Amount is 116, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₆

∴ If the Amount is 3828, then the Principal = ¹⁰⁰/₁₁₆ × 3828

= ^{100 × 3828}/₁₁₆

= ³⁸²⁸⁰⁰/₁₁₆

= 3300

Thus, Principal = $3300

Thus, the sum borrowed = $3300 Answer

Similar Questions

(1) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $8280 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 4% simple interest.

(3) Calculate the amount due if Thomas borrowed a sum of $3800 at 7% simple interest for 3 years.

(4) Calculate the amount due if Michael borrowed a sum of $3300 at 8% simple interest for 4 years.

(5) Calculate the amount due if Jennifer borrowed a sum of $3250 at 3% simple interest for 3 years.

(6) Find the amount to be paid if Jessica borrowed a sum of $5750 at 3% simple interest for 7 years.

(7) In how much time a principal of $3150 will amount to $3780 at a simple interest of 5% per annum?

(8) Calculate the amount due if Karen borrowed a sum of $3950 at 7% simple interest for 3 years.

(9) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $9372 to clear the loan, then find the time period of the loan.

(10) How much loan did William borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6325 to clear it?