Simple Interest
Math MCQs

Question :    If John paid $3584 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

Correct Answer  $3200

Solution & Explanation

Solution

Given,

Amount (A) = $3584

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

$3584 = P (1 + 3% × 4)

⇒ $3584 = P (1 + ³/₁₀₀ × 4)

⇒ $3584 = P (1 + ^{3 × 4}/₁₀₀)

⇒ $3584 = P (1 + ¹²/₁₀₀)

⇒ $3584 = P (^{100 + 12}/₁₀₀)

⇒ $3584 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $3584

⇒ P = ³⁵⁸⁴/_¹¹²/100

⇒ P = 3584 × ¹⁰⁰/₁₁₂

⇒ P = ^{3584 × 100}/₁₁₂

⇒ P = ³⁵⁸⁴⁰⁰/₁₁₂

⇒ P = $3200

Thus, the sum borrowed (P) = $3200 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 3584, then the Principal = ¹⁰⁰/₁₁₂ × 3584

= ^{100 × 3584}/₁₁₂

= ³⁵⁸⁴⁰⁰/₁₁₂

= 3200

Thus, Principal = $3200

Thus, the sum borrowed = $3200 Answer

Similar Questions

(1) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 7% simple interest?

(2) Calculate the amount due if Mary borrowed a sum of $3050 at 6% simple interest for 3 years.

(3) If Andrew paid $5760 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(4) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 10% simple interest?

(5) 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.

(6) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 8% simple interest.

(7) In how much time a principal of $3000 will amount to $3240 at a simple interest of 2% per annum?

(8) Find the amount to be paid if Mary borrowed a sum of $5050 at 6% simple interest for 8 years.

(9) Calculate the amount due if Richard borrowed a sum of $3600 at 7% simple interest for 4 years.

(10) Lisa had to pay $4414.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.