Simple Interest
Math MCQs

Question :    If Robert paid $3472 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

Correct Answer  $3100

Solution & Explanation

Solution

Given,

Amount (A) = $3472

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

$3472 = P (1 + 3% × 4)

⇒ $3472 = P (1 + ³/₁₀₀ × 4)

⇒ $3472 = P (1 + ^{3 × 4}/₁₀₀)

⇒ $3472 = P (1 + ¹²/₁₀₀)

⇒ $3472 = P (^{100 + 12}/₁₀₀)

⇒ $3472 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $3472

⇒ P = ³⁴⁷²/_¹¹²/100

⇒ P = 3472 × ¹⁰⁰/₁₁₂

⇒ P = ^{3472 × 100}/₁₁₂

⇒ P = ³⁴⁷²⁰⁰/₁₁₂

⇒ P = $3100

Thus, the sum borrowed (P) = $3100 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 3472, then the Principal = ¹⁰⁰/₁₁₂ × 3472

= ^{100 × 3472}/₁₁₂

= ³⁴⁷²⁰⁰/₁₁₂

= 3100

Thus, Principal = $3100

Thus, the sum borrowed = $3100 Answer

Similar Questions

(1) In how much time a principal of $3000 will amount to $3450 at a simple interest of 3% per annum?

(2) How much loan did Deborah borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9312.5 to clear it?

(3) Michael had to pay $3498 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(4) Calculate the amount due if Mary borrowed a sum of $3050 at 10% simple interest for 4 years.

(5) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 10% simple interest?

(6) What amount does William have to pay after 6 years if he takes a loan of $3500 at 3% simple interest?

(7) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 6% simple interest?

(8) In how much time a principal of $3000 will amount to $3120 at a simple interest of 2% per annum?

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

(10) If Nancy paid $4980 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.