Simple Interest
Math MCQs

Question :    Richard had to pay $3816 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  $3600

Solution & Explanation

Solution

Given,

Amount (A) = $3816

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

$3816 = P (1 + 2% × 3)

⇒ $3816 = P (1 + ²/₁₀₀ × 3)

⇒ $3816 = P (1 + ^{2 × 3}/₁₀₀)

⇒ $3816 = P (1 + ⁶/₁₀₀)

⇒ $3816 = P (^{100 + 6}/₁₀₀)

⇒ $3816 = P × ¹⁰⁶/₁₀₀

⇒ P × ¹⁰⁶/₁₀₀ = $3816

⇒ P = ³⁸¹⁶/_¹⁰⁶/100

⇒ P = 3816 × ¹⁰⁰/₁₀₆

⇒ P = ^{3816 × 100}/₁₀₆

⇒ P = ³⁸¹⁶⁰⁰/₁₀₆

⇒ P = $3600

Thus, the sum borrowed (P) = $3600 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 3816, then the Principal = ¹⁰⁰/₁₀₆ × 3816

= ^{100 × 3816}/₁₀₆

= ³⁸¹⁶⁰⁰/₁₀₆

= 3600

Thus, Principal = $3600

Thus, the sum borrowed = $3600 Answer

Similar Questions

(1) James had to pay $3450 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(2) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $8944 to clear the loan, then find the time period of the loan.

(3) If Elizabeth borrowed $3450 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(4) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $11590 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 8% simple interest.

(6) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $7252 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due if David borrowed a sum of $3400 at 3% simple interest for 3 years.

(8) Find the amount to be paid if Mary borrowed a sum of $5050 at 6% simple interest for 7 years.

(9) Calculate the amount due if Mary borrowed a sum of $3050 at 3% simple interest for 4 years.

(10) If Joshua paid $5292 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.