Simple Interest
Math MCQs

Question :    If Thomas paid $4256 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

Correct Answer  $3800

Solution & Explanation

Solution

Given,

Amount (A) = $4256

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

$4256 = P (1 + 3% × 4)

⇒ $4256 = P (1 + ³/₁₀₀ × 4)

⇒ $4256 = P (1 + ^{3 × 4}/₁₀₀)

⇒ $4256 = P (1 + ¹²/₁₀₀)

⇒ $4256 = P (^{100 + 12}/₁₀₀)

⇒ $4256 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $4256

⇒ P = ⁴²⁵⁶/_¹¹²/100

⇒ P = 4256 × ¹⁰⁰/₁₁₂

⇒ P = ^{4256 × 100}/₁₁₂

⇒ P = ⁴²⁵⁶⁰⁰/₁₁₂

⇒ P = $3800

Thus, the sum borrowed (P) = $3800 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 4256, then the Principal = ¹⁰⁰/₁₁₂ × 4256

= ^{100 × 4256}/₁₁₂

= ⁴²⁵⁶⁰⁰/₁₁₂

= 3800

Thus, Principal = $3800

Thus, the sum borrowed = $3800 Answer

Similar Questions

(1) Daniel had to pay $4592 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(2) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 6% simple interest.

(3) Find the amount to be paid if Jessica borrowed a sum of $5750 at 10% simple interest for 8 years.

(4) If Betty paid $4760 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(5) Calculate the amount due if James borrowed a sum of $3000 at 6% simple interest for 3 years.

(6) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.

(7) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $6854 to clear the loan, then find the time period of the loan.

(8) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 4% simple interest?

(9) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $10080 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due if James borrowed a sum of $3000 at 5% simple interest for 4 years.