Simple Interest
Math MCQs

Question :    If William paid $4060 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

Correct Answer  $3500

Solution & Explanation

Solution

Given,

Amount (A) = $4060

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

$4060 = P (1 + 4% × 4)

⇒ $4060 = P (1 + ⁴/₁₀₀ × 4)

⇒ $4060 = P (1 + ^{4 × 4}/₁₀₀)

⇒ $4060 = P (1 + ¹⁶/₁₀₀)

⇒ $4060 = P (^{100 + 16}/₁₀₀)

⇒ $4060 = P × ¹¹⁶/₁₀₀

⇒ P × ¹¹⁶/₁₀₀ = $4060

⇒ P = ⁴⁰⁶⁰/_¹¹⁶/100

⇒ P = 4060 × ¹⁰⁰/₁₁₆

⇒ P = ^{4060 × 100}/₁₁₆

⇒ P = ⁴⁰⁶⁰⁰⁰/₁₁₆

⇒ P = $3500

Thus, the sum borrowed (P) = $3500 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 4060, then the Principal = ¹⁰⁰/₁₁₆ × 4060

= ^{100 × 4060}/₁₁₆

= ⁴⁰⁶⁰⁰⁰/₁₁₆

= 3500

Thus, Principal = $3500

Thus, the sum borrowed = $3500 Answer

Similar Questions

(1) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $10332 to clear the loan, then find the time period of the loan.

(2) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $9360 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 4% simple interest.

(4) 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?

(5) If David borrowed $3400 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(6) In how much time a principal of $3150 will amount to $3339 at a simple interest of 2% per annum?

(7) Calculate the amount due if Susan borrowed a sum of $3650 at 9% simple interest for 3 years.

(8) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 6% simple interest.

(9) In how much time a principal of $3050 will amount to $3416 at a simple interest of 4% per annum?

(10) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 6% simple interest.