Simple Interest
Math MCQs

Question :    If Steven paid $5336 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

Correct Answer  $4600

Solution & Explanation

Solution

Given,

Amount (A) = $5336

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

$5336 = P (1 + 4% × 4)

⇒ $5336 = P (1 + ⁴/₁₀₀ × 4)

⇒ $5336 = P (1 + ^{4 × 4}/₁₀₀)

⇒ $5336 = P (1 + ¹⁶/₁₀₀)

⇒ $5336 = P (^{100 + 16}/₁₀₀)

⇒ $5336 = P × ¹¹⁶/₁₀₀

⇒ P × ¹¹⁶/₁₀₀ = $5336

⇒ P = ⁵³³⁶/_¹¹⁶/100

⇒ P = 5336 × ¹⁰⁰/₁₁₆

⇒ P = ^{5336 × 100}/₁₁₆

⇒ P = ⁵³³⁶⁰⁰/₁₁₆

⇒ P = $4600

Thus, the sum borrowed (P) = $4600 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 5336, then the Principal = ¹⁰⁰/₁₁₆ × 5336

= ^{100 × 5336}/₁₁₆

= ⁵³³⁶⁰⁰/₁₁₆

= 4600

Thus, Principal = $4600

Thus, the sum borrowed = $4600 Answer

Similar Questions

(1) Calculate the amount due if Patricia borrowed a sum of $3150 at 3% simple interest for 3 years.

(2) In how much time a principal of $3150 will amount to $3465 at a simple interest of 5% per annum?

(3) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 10% simple interest?

(4) Calculate the amount due if Karen borrowed a sum of $3950 at 2% simple interest for 4 years.

(5) Calculate the amount due if William borrowed a sum of $3500 at 9% simple interest for 4 years.

(6) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 7% simple interest.

(7) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 3% simple interest.

(8) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $11200 to clear the loan, then find the time period of the loan.

(9) If Joshua paid $5292 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(10) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $9514 to clear the loan, then find the time period of the loan.