Simple Interest
Math MCQs

Question :    If James paid $3360 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

Correct Answer  $3000

Solution & Explanation

Solution

Given,

Amount (A) = $3360

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

$3360 = P (1 + 3% × 4)

⇒ $3360 = P (1 + ³/₁₀₀ × 4)

⇒ $3360 = P (1 + ^{3 × 4}/₁₀₀)

⇒ $3360 = P (1 + ¹²/₁₀₀)

⇒ $3360 = P (^{100 + 12}/₁₀₀)

⇒ $3360 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $3360

⇒ P = ³³⁶⁰/_¹¹²/100

⇒ P = 3360 × ¹⁰⁰/₁₁₂

⇒ P = ^{3360 × 100}/₁₁₂

⇒ P = ³³⁶⁰⁰⁰/₁₁₂

⇒ P = $3000

Thus, the sum borrowed (P) = $3000 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 3360, then the Principal = ¹⁰⁰/₁₁₂ × 3360

= ^{100 × 3360}/₁₁₂

= ³³⁶⁰⁰⁰/₁₁₂

= 3000

Thus, Principal = $3000

Thus, the sum borrowed = $3000 Answer

Similar Questions

(1) Calculate the amount due if William borrowed a sum of $3500 at 7% simple interest for 4 years.

(2) In how much time a principal of $3100 will amount to $3286 at a simple interest of 2% per annum?

(3) If David borrowed $3400 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(4) What amount does David have to pay after 5 years if he takes a loan of $3400 at 8% simple interest?

(5) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 4% simple interest?

(6) Find the amount to be paid if John borrowed a sum of $5200 at 6% simple interest for 8 years.

(7) Calculate the amount due if Barbara borrowed a sum of $3550 at 4% simple interest for 4 years.

(8) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 4% simple interest?

(9) How much loan did Brian borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8280 to clear it?

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