Simple Interest
Math MCQs

Question :    If Jennifer paid $3640 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

Correct Answer  $3250

Solution & Explanation

Solution

Given,

Amount (A) = $3640

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

$3640 = P (1 + 3% × 4)

⇒ $3640 = P (1 + ³/₁₀₀ × 4)

⇒ $3640 = P (1 + ^{3 × 4}/₁₀₀)

⇒ $3640 = P (1 + ¹²/₁₀₀)

⇒ $3640 = P (^{100 + 12}/₁₀₀)

⇒ $3640 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $3640

⇒ P = ³⁶⁴⁰/_¹¹²/100

⇒ P = 3640 × ¹⁰⁰/₁₁₂

⇒ P = ^{3640 × 100}/₁₁₂

⇒ P = ³⁶⁴⁰⁰⁰/₁₁₂

⇒ P = $3250

Thus, the sum borrowed (P) = $3250 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 3640, then the Principal = ¹⁰⁰/₁₁₂ × 3640

= ^{100 × 3640}/₁₁₂

= ³⁶⁴⁰⁰⁰/₁₁₂

= 3250

Thus, Principal = $3250

Thus, the sum borrowed = $3250 Answer

Similar Questions

(1) Calculate the amount due if Jessica borrowed a sum of $3750 at 2% simple interest for 3 years.

(2) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 8% simple interest.

(3) Thomas had to pay $4256 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(4) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 3% simple interest.

(5) 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.

(6) Michelle had to pay $5692.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(7) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $8046 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due if Christopher borrowed a sum of $4000 at 9% simple interest for 3 years.

(9) If Anthony paid $4816 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(10) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $9617 to clear the loan, then find the time period of the loan.