Simple Interest
Math MCQs

Question :    If Susan paid $4234 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

Correct Answer  $3650

Solution & Explanation

Solution

Given,

Amount (A) = $4234

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

$4234 = P (1 + 4% × 4)

⇒ $4234 = P (1 + ⁴/₁₀₀ × 4)

⇒ $4234 = P (1 + ^{4 × 4}/₁₀₀)

⇒ $4234 = P (1 + ¹⁶/₁₀₀)

⇒ $4234 = P (^{100 + 16}/₁₀₀)

⇒ $4234 = P × ¹¹⁶/₁₀₀

⇒ P × ¹¹⁶/₁₀₀ = $4234

⇒ P = ⁴²³⁴/_¹¹⁶/100

⇒ P = 4234 × ¹⁰⁰/₁₁₆

⇒ P = ^{4234 × 100}/₁₁₆

⇒ P = ⁴²³⁴⁰⁰/₁₁₆

⇒ P = $3650

Thus, the sum borrowed (P) = $3650 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 4234, then the Principal = ¹⁰⁰/₁₁₆ × 4234

= ^{100 × 4234}/₁₁₆

= ⁴²³⁴⁰⁰/₁₁₆

= 3650

Thus, Principal = $3650

Thus, the sum borrowed = $3650 Answer

Similar Questions

(1) In how much time a principal of $3200 will amount to $3392 at a simple interest of 3% per annum?

(2) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $8732 to clear the loan, then find the time period of the loan.

(3) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $10200 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due if Thomas borrowed a sum of $3800 at 9% simple interest for 4 years.

(5) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 10% simple interest.

(6) Find the amount to be paid if John borrowed a sum of $5200 at 8% simple interest for 8 years.

(7) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 5% simple interest?

(8) Find the amount to be paid if Joseph borrowed a sum of $5700 at 8% simple interest for 8 years.

(9) If Emily paid $5320 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(10) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $8360 to clear the loan, then find the time period of the loan.