Simple Interest
Math MCQs

Question :    If Nancy paid $4648 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

Correct Answer  $4150

Solution & Explanation

Solution

Given,

Amount (A) = $4648

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

$4648 = P (1 + 3% × 4)

⇒ $4648 = P (1 + ³/₁₀₀ × 4)

⇒ $4648 = P (1 + ^{3 × 4}/₁₀₀)

⇒ $4648 = P (1 + ¹²/₁₀₀)

⇒ $4648 = P (^{100 + 12}/₁₀₀)

⇒ $4648 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $4648

⇒ P = ⁴⁶⁴⁸/_¹¹²/100

⇒ P = 4648 × ¹⁰⁰/₁₁₂

⇒ P = ^{4648 × 100}/₁₁₂

⇒ P = ⁴⁶⁴⁸⁰⁰/₁₁₂

⇒ P = $4150

Thus, the sum borrowed (P) = $4150 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 4648, then the Principal = ¹⁰⁰/₁₁₂ × 4648

= ^{100 × 4648}/₁₁₂

= ⁴⁶⁴⁸⁰⁰/₁₁₂

= 4150

Thus, Principal = $4150

Thus, the sum borrowed = $4150 Answer

Similar Questions

(1) If Christopher borrowed $4000 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(2) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $7700 to clear the loan, then find the time period of the loan.

(3) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 2% simple interest for 8 years.

(4) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 2% simple interest.

(5) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $10080 to clear the loan, then find the time period of the loan.

(6) Susan had to pay $4197.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(7) Calculate the amount due if David borrowed a sum of $3400 at 10% simple interest for 4 years.

(8) If Karen borrowed $3950 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(9) If Donna paid $5238 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(10) Find the amount to be paid if Thomas borrowed a sum of $5800 at 9% simple interest for 7 years.