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) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 3% simple interest.

(2) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 3% simple interest.

(3) Calculate the amount due if Thomas borrowed a sum of $3800 at 6% simple interest for 3 years.

(4) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 3% simple interest?

(5) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 7% simple interest.

(6) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $7696 to clear the loan, then find the time period of the loan.

(7) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $8170 to clear the loan, then find the time period of the loan.

(8) Find the amount to be paid if Robert borrowed a sum of $5100 at 4% simple interest for 7 years.

(9) Find the amount to be paid if John borrowed a sum of $5200 at 7% simple interest for 7 years.

(10) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6106 to clear the loan, then find the time period of the loan.