Simple Interest
Math MCQs

Question :    If Richard paid $4176 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

Correct Answer  $3600

Solution & Explanation

Solution

Given,

Amount (A) = $4176

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

$4176 = P (1 + 4% × 4)

⇒ $4176 = P (1 + ⁴/₁₀₀ × 4)

⇒ $4176 = P (1 + ^{4 × 4}/₁₀₀)

⇒ $4176 = P (1 + ¹⁶/₁₀₀)

⇒ $4176 = P (^{100 + 16}/₁₀₀)

⇒ $4176 = P × ¹¹⁶/₁₀₀

⇒ P × ¹¹⁶/₁₀₀ = $4176

⇒ P = ⁴¹⁷⁶/_¹¹⁶/100

⇒ P = 4176 × ¹⁰⁰/₁₁₆

⇒ P = ^{4176 × 100}/₁₁₆

⇒ P = ⁴¹⁷⁶⁰⁰/₁₁₆

⇒ P = $3600

Thus, the sum borrowed (P) = $3600 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 4176, then the Principal = ¹⁰⁰/₁₁₆ × 4176

= ^{100 × 4176}/₁₁₆

= ⁴¹⁷⁶⁰⁰/₁₁₆

= 3600

Thus, Principal = $3600

Thus, the sum borrowed = $3600 Answer

Similar Questions

(1) Find the amount to be paid if William borrowed a sum of $5500 at 2% simple interest for 7 years.

(2) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $7668 to clear the loan, then find the time period of the loan.

(3) What amount will be due after 2 years if David borrowed a sum of $3200 at a 7% simple interest?

(4) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $7400 to clear the loan, then find the time period of the loan.

(5) If Christopher paid $4640 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(6) Find the amount to be paid if Joseph borrowed a sum of $5700 at 2% simple interest for 7 years.

(7) Calculate the amount due if Richard borrowed a sum of $3600 at 7% simple interest for 4 years.

(8) Find the amount to be paid if Mary borrowed a sum of $5050 at 9% simple interest for 7 years.

(9) Calculate the amount due if Thomas borrowed a sum of $3800 at 6% simple interest for 3 years.

(10) If Barbara borrowed $3550 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.