Simple Interest
Math MCQs

Question :    If Linda paid $3886 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

Correct Answer  $3350

Solution & Explanation

Solution

Given,

Amount (A) = $3886

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

$3886 = P (1 + 4% × 4)

⇒ $3886 = P (1 + ⁴/₁₀₀ × 4)

⇒ $3886 = P (1 + ^{4 × 4}/₁₀₀)

⇒ $3886 = P (1 + ¹⁶/₁₀₀)

⇒ $3886 = P (^{100 + 16}/₁₀₀)

⇒ $3886 = P × ¹¹⁶/₁₀₀

⇒ P × ¹¹⁶/₁₀₀ = $3886

⇒ P = ³⁸⁸⁶/_¹¹⁶/100

⇒ P = 3886 × ¹⁰⁰/₁₁₆

⇒ P = ^{3886 × 100}/₁₁₆

⇒ P = ³⁸⁸⁶⁰⁰/₁₁₆

⇒ P = $3350

Thus, the sum borrowed (P) = $3350 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 3886, then the Principal = ¹⁰⁰/₁₁₆ × 3886

= ^{100 × 3886}/₁₁₆

= ³⁸⁸⁶⁰⁰/₁₁₆

= 3350

Thus, Principal = $3350

Thus, the sum borrowed = $3350 Answer

Similar Questions

(1) How much loan did Mary borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6312.5 to clear it?

(2) Barbara had to pay $3869.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(3) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 9% simple interest.

(4) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 4% simple interest.

(5) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $7824 to clear the loan, then find the time period of the loan.

(6) If Thomas paid $4256 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(7) In how much time a principal of $3200 will amount to $3680 at a simple interest of 3% per annum?

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

(9) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $7990 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 2% simple interest.