Simple Interest
Math MCQs

Question :    If Joseph paid $4292 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

Correct Answer  $3700

Solution & Explanation

Solution

Given,

Amount (A) = $4292

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

$4292 = P (1 + 4% × 4)

⇒ $4292 = P (1 + ⁴/₁₀₀ × 4)

⇒ $4292 = P (1 + ^{4 × 4}/₁₀₀)

⇒ $4292 = P (1 + ¹⁶/₁₀₀)

⇒ $4292 = P (^{100 + 16}/₁₀₀)

⇒ $4292 = P × ¹¹⁶/₁₀₀

⇒ P × ¹¹⁶/₁₀₀ = $4292

⇒ P = ⁴²⁹²/_¹¹⁶/100

⇒ P = 4292 × ¹⁰⁰/₁₁₆

⇒ P = ^{4292 × 100}/₁₁₆

⇒ P = ⁴²⁹²⁰⁰/₁₁₆

⇒ P = $3700

Thus, the sum borrowed (P) = $3700 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 4292, then the Principal = ¹⁰⁰/₁₁₆ × 4292

= ^{100 × 4292}/₁₁₆

= ⁴²⁹²⁰⁰/₁₁₆

= 3700

Thus, Principal = $3700

Thus, the sum borrowed = $3700 Answer

Similar Questions

(1) How much loan did Michael borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6095 to clear it?

(2) Find the amount to be paid if John borrowed a sum of $5200 at 6% simple interest for 8 years.

(3) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $8732 to clear the loan, then find the time period of the loan.

(4) How much loan did Barbara borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6660 to clear it?

(5) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $11390 to clear the loan, then find the time period of the loan.

(6) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $10281 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 8% simple interest.

(8) In how much time a principal of $3000 will amount to $3450 at a simple interest of 3% per annum?

(9) Find the amount to be paid if David borrowed a sum of $5400 at 4% simple interest for 8 years.

(10) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 7% simple interest.