Simple Interest
Math MCQs

Question :    If Ashley paid $5096 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

Correct Answer  $4550

Solution & Explanation

Solution

Given,

Amount (A) = $5096

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

$5096 = P (1 + 3% × 4)

⇒ $5096 = P (1 + ³/₁₀₀ × 4)

⇒ $5096 = P (1 + ^{3 × 4}/₁₀₀)

⇒ $5096 = P (1 + ¹²/₁₀₀)

⇒ $5096 = P (^{100 + 12}/₁₀₀)

⇒ $5096 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $5096

⇒ P = ⁵⁰⁹⁶/_¹¹²/100

⇒ P = 5096 × ¹⁰⁰/₁₁₂

⇒ P = ^{5096 × 100}/₁₁₂

⇒ P = ⁵⁰⁹⁶⁰⁰/₁₁₂

⇒ P = $4550

Thus, the sum borrowed (P) = $4550 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 5096, then the Principal = ¹⁰⁰/₁₁₂ × 5096

= ^{100 × 5096}/₁₁₂

= ⁵⁰⁹⁶⁰⁰/₁₁₂

= 4550

Thus, Principal = $4550

Thus, the sum borrowed = $4550 Answer

Similar Questions

(1) How much loan did Christopher borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7200 to clear it?

(2) How much loan did Deborah borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8940 to clear it?

(3) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $9983 to clear the loan, then find the time period of the loan.

(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 Joseph borrowed a sum of $3700 at 9% simple interest for 3 years.

(6) Find the amount to be paid if Patricia borrowed a sum of $5150 at 5% simple interest for 7 years.

(7) How much loan did Jacob borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9200 to clear it?

(8) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $6560 to clear the loan, then find the time period of the loan.

(9) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $11400 to clear the loan, then find the time period of the loan.

(10) Charles took a loan of $5800 at the rate of 8% simple interest per annum. If he paid an amount of $9048 to clear the loan, then find the time period of the loan.