Simple Interest
Math MCQs

Question :    Sarah had to pay $4081 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  $3850

Solution & Explanation

Solution

Given,

Amount (A) = $4081

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

$4081 = P (1 + 2% × 3)

⇒ $4081 = P (1 + ²/₁₀₀ × 3)

⇒ $4081 = P (1 + ^{2 × 3}/₁₀₀)

⇒ $4081 = P (1 + ⁶/₁₀₀)

⇒ $4081 = P (^{100 + 6}/₁₀₀)

⇒ $4081 = P × ¹⁰⁶/₁₀₀

⇒ P × ¹⁰⁶/₁₀₀ = $4081

⇒ P = ⁴⁰⁸¹/_¹⁰⁶/100

⇒ P = 4081 × ¹⁰⁰/₁₀₆

⇒ P = ^{4081 × 100}/₁₀₆

⇒ P = ⁴⁰⁸¹⁰⁰/₁₀₆

⇒ P = $3850

Thus, the sum borrowed (P) = $3850 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 4081, then the Principal = ¹⁰⁰/₁₀₆ × 4081

= ^{100 × 4081}/₁₀₆

= ⁴⁰⁸¹⁰⁰/₁₀₆

= 3850

Thus, Principal = $3850

Thus, the sum borrowed = $3850 Answer

Similar Questions

(1) Calculate the amount due if John borrowed a sum of $3200 at 9% simple interest for 4 years.

(2) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $8330 to clear the loan, then find the time period of the loan.

(3) If Patricia paid $3528 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(4) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $7661 to clear the loan, then find the time period of the loan.

(5) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 6% simple interest?

(6) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 10% simple interest for 8 years.

(7) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $9394 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 8% simple interest.

(9) Find the amount to be paid if Christopher borrowed a sum of $6000 at 8% simple interest for 8 years.

(10) Calculate the amount due if Richard borrowed a sum of $3600 at 6% simple interest for 3 years.