Simple Interest
Math MCQs

Question :    If Charles paid $4368 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

Correct Answer  $3900

Solution & Explanation

Solution

Given,

Amount (A) = $4368

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

$4368 = P (1 + 3% × 4)

⇒ $4368 = P (1 + ³/₁₀₀ × 4)

⇒ $4368 = P (1 + ^{3 × 4}/₁₀₀)

⇒ $4368 = P (1 + ¹²/₁₀₀)

⇒ $4368 = P (^{100 + 12}/₁₀₀)

⇒ $4368 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $4368

⇒ P = ⁴³⁶⁸/_¹¹²/100

⇒ P = 4368 × ¹⁰⁰/₁₁₂

⇒ P = ^{4368 × 100}/₁₁₂

⇒ P = ⁴³⁶⁸⁰⁰/₁₁₂

⇒ P = $3900

Thus, the sum borrowed (P) = $3900 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 4368, then the Principal = ¹⁰⁰/₁₁₂ × 4368

= ^{100 × 4368}/₁₁₂

= ⁴³⁶⁸⁰⁰/₁₁₂

= 3900

Thus, Principal = $3900

Thus, the sum borrowed = $3900 Answer

Similar Questions

(1) In how much time a principal of $3100 will amount to $3348 at a simple interest of 4% per annum?

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

(3) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 7% simple interest.

(4) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 9% simple interest.

(5) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $5984 to clear the loan, then find the time period of the loan.

(6) How much loan did Brian borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7920 to clear it?

(7) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 5% simple interest?

(8) Calculate the amount due if Susan borrowed a sum of $3650 at 9% simple interest for 4 years.

(9) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 7% simple interest.

(10) If Richard borrowed $3600 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.