Simple Interest
Math MCQs

Question :    If Elizabeth paid $3864 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

Correct Answer  $3450

Solution & Explanation

Solution

Given,

Amount (A) = $3864

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

$3864 = P (1 + 3% × 4)

⇒ $3864 = P (1 + ³/₁₀₀ × 4)

⇒ $3864 = P (1 + ^{3 × 4}/₁₀₀)

⇒ $3864 = P (1 + ¹²/₁₀₀)

⇒ $3864 = P (^{100 + 12}/₁₀₀)

⇒ $3864 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $3864

⇒ P = ³⁸⁶⁴/_¹¹²/100

⇒ P = 3864 × ¹⁰⁰/₁₁₂

⇒ P = ^{3864 × 100}/₁₁₂

⇒ P = ³⁸⁶⁴⁰⁰/₁₁₂

⇒ P = $3450

Thus, the sum borrowed (P) = $3450 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 3864, then the Principal = ¹⁰⁰/₁₁₂ × 3864

= ^{100 × 3864}/₁₁₂

= ³⁸⁶⁴⁰⁰/₁₁₂

= 3450

Thus, Principal = $3450

Thus, the sum borrowed = $3450 Answer

Similar Questions

(1) Find the amount to be paid if Richard borrowed a sum of $5600 at 8% simple interest for 8 years.

(2) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 5% simple interest?

(3) How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8580 to clear it?

(4) Find the amount to be paid if Richard borrowed a sum of $5600 at 10% simple interest for 8 years.

(5) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 3% simple interest?

(6) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 4% simple interest.

(7) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 9% simple interest?

(8) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 7% simple interest.

(9) Find the amount to be paid if Jessica borrowed a sum of $5750 at 9% simple interest for 7 years.

(10) How much loan did Laura borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8635 to clear it?