Simple Interest
Math MCQs

Question :    If David paid $3808 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

Correct Answer  $3400

Solution & Explanation

Solution

Given,

Amount (A) = $3808

Rate of Simple Interest (R) = 3%

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

$3808 = P (1 + 3% × 4)

⇒ $3808 = P (1 + ³/₁₀₀ × 4)

⇒ $3808 = P (1 + ^{3 × 4}/₁₀₀)

⇒ $3808 = P (1 + ¹²/₁₀₀)

⇒ $3808 = P (^{100 + 12}/₁₀₀)

⇒ $3808 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $3808

⇒ P = ³⁸⁰⁸/_¹¹²/100

⇒ P = 3808 × ¹⁰⁰/₁₁₂

⇒ P = ^{3808 × 100}/₁₁₂

⇒ P = ³⁸⁰⁸⁰⁰/₁₁₂

⇒ P = $3400

Thus, the sum borrowed (P) = $3400 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 = 3% per annum

Thus, Interest = 3% of principal

⇒ Interest = 3% of 100 = 3

Thus, Simple Interest for 1 year = 3

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 × 3 = 12

Thus, simple interest for 4 years = 12

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 12 = 112

Calculation of the Principal

Now,

∵ If the Amount is 112, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₂

∴ If the Amount is 3808, then the Principal = ¹⁰⁰/₁₁₂ × 3808

= ^{100 × 3808}/₁₁₂

= ³⁸⁰⁸⁰⁰/₁₁₂

= 3400

Thus, Principal = $3400

Thus, the sum borrowed = $3400 Answer

Similar Questions

(1) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 2% simple interest?

(2) In how much time a principal of $3150 will amount to $3433.5 at a simple interest of 3% per annum?

(3) Calculate the amount due if Sarah borrowed a sum of $3850 at 4% simple interest for 4 years.

(4) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $6956 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due if Karen borrowed a sum of $3950 at 6% simple interest for 3 years.

(6) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 7% simple interest.

(7) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $8296 to clear the loan, then find the time period of the loan.

(8) 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.

(9) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 8% simple interest?

(10) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $9116 to clear the loan, then find the time period of the loan.