Simple Interest
Math MCQs

Question :    If Mark paid $5104 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

Correct Answer  $4400

Solution & Explanation

Solution

Given,

Amount (A) = $5104

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

$5104 = P (1 + 4% × 4)

⇒ $5104 = P (1 + ⁴/₁₀₀ × 4)

⇒ $5104 = P (1 + ^{4 × 4}/₁₀₀)

⇒ $5104 = P (1 + ¹⁶/₁₀₀)

⇒ $5104 = P (^{100 + 16}/₁₀₀)

⇒ $5104 = P × ¹¹⁶/₁₀₀

⇒ P × ¹¹⁶/₁₀₀ = $5104

⇒ P = ⁵¹⁰⁴/_¹¹⁶/100

⇒ P = 5104 × ¹⁰⁰/₁₁₆

⇒ P = ^{5104 × 100}/₁₁₆

⇒ P = ⁵¹⁰⁴⁰⁰/₁₁₆

⇒ 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 = 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 5104, then the Principal = ¹⁰⁰/₁₁₆ × 5104

= ^{100 × 5104}/₁₁₆

= ⁵¹⁰⁴⁰⁰/₁₁₆

= 4400

Thus, Principal = $4400

Thus, the sum borrowed = $4400 Answer

Similar Questions

(1) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 2% simple interest for 4 years.

(2) Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $7526 to clear the loan, then find the time period of the loan.

(3) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 9% simple interest?

(4) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $7480 to clear the loan, then find the time period of the loan.

(5) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $13110 to clear the loan, then find the time period of the loan.

(6) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $9632 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 9% simple interest.

(8) If Mary borrowed $3050 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(9) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 4% simple interest?

(10) Find the amount to be paid if Thomas borrowed a sum of $5800 at 7% simple interest for 7 years.