Simple Interest
Math MCQs

Question :    Karen had to pay $4187 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

Correct Answer  $3950

Solution & Explanation

Solution

Given,

Amount (A) = $4187

Rate of Simple Interest (R) = 2%

Time (T) = 3 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

$4187 = P (1 + 2% × 3)

⇒ $4187 = P (1 + ²/₁₀₀ × 3)

⇒ $4187 = P (1 + ^{2 × 3}/₁₀₀)

⇒ $4187 = P (1 + ⁶/₁₀₀)

⇒ $4187 = P (^{100 + 6}/₁₀₀)

⇒ $4187 = P × ¹⁰⁶/₁₀₀

⇒ P × ¹⁰⁶/₁₀₀ = $4187

⇒ P = ⁴¹⁸⁷/_¹⁰⁶/100

⇒ P = 4187 × ¹⁰⁰/₁₀₆

⇒ P = ^{4187 × 100}/₁₀₆

⇒ P = ⁴¹⁸⁷⁰⁰/₁₀₆

⇒ P = $3950

Thus, the sum borrowed (P) = $3950 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 = 2% per annum

Thus, Interest = 2% of principal

⇒ Interest = 2% of 100 = 2

Thus, Simple Interest for 1 year = 2

Calculation of the Amount

Since, in the question, time = 3 years

So, we need to calculate the simple interest for the given time period, which is 3 years

Thus, Simple Interest for 3 years = 3 × Simple Interest for 1 year

= 3 × 2 = 6

Thus, simple interest for 3 years = 6

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 6 = 106

Calculation of the Principal

Now,

∵ If the Amount is 106, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₀₆

∴ If the Amount is 4187, then the Principal = ¹⁰⁰/₁₀₆ × 4187

= ^{100 × 4187}/₁₀₆

= ⁴¹⁸⁷⁰⁰/₁₀₆

= 3950

Thus, Principal = $3950

Thus, the sum borrowed = $3950 Answer

Similar Questions

(1) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $7548 to clear the loan, then find the time period of the loan.

(2) If Charles borrowed $3900 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(3) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 7% simple interest.

(4) If Elizabeth paid $4002 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(5) Calculate the amount due if William borrowed a sum of $3500 at 2% simple interest for 3 years.

(6) Find the amount to be paid if Patricia borrowed a sum of $5150 at 10% simple interest for 8 years.

(7) Calculate the amount due if Thomas borrowed a sum of $3800 at 10% simple interest for 4 years.

(8) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $9620 to clear the loan, then find the time period of the loan.

(9) How much loan did Joshua borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8625 to clear it?

(10) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 4% simple interest for 7 years.