Simple Interest
MCQs Math


Question:     If Richard paid $4176 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.


Correct Answer  $3600

Solution And Explanation

Solution

Given,

Amount (A) = $4176

Rate of Simple Interest (R) = 4%

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

$4176 = P (1 + 4% × 4)

⇒ $4176 = P (1 + 4/100 × 4)

⇒ $4176 = P (1 + 4 × 4/100)

⇒ $4176 = P (1 + 16/100)

⇒ $4176 = P (100 + 16/100)

⇒ $4176 = P × 116/100

⇒ P × 116/100 = $4176

⇒ P = 4176/116/100

⇒ P = 4176 × 100/116

⇒ P = 4176 × 100/116

⇒ P = 417600/116

⇒ P = $3600

Thus, the sum borrowed (P) = $3600 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 = 4% per annum

Thus, Interest = 4% of principal

⇒ Interest = 4% of 100 = 4

Thus, Simple Interest for 1 year = 4

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 × 4 = 16

Thus, simple interest for 4 years = 16

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 16 = 116

Calculation of the Principal

Now,

∵ If the Amount is 116, then the Principal = 100

∴ If the Amount is 1, then the Principal = 100/116

∴ If the Amount is 4176, then the Principal = 100/116 × 4176

= 100 × 4176/116

= 417600/116

= 3600

Thus, Principal = $3600

Thus, the sum borrowed = $3600 Answer


Similar Questions

(1) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $9360 to clear the loan, then find the time period of the loan.

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

(3) Find the amount to be paid if Jessica borrowed a sum of $5750 at 8% simple interest for 7 years.

(4) Find the amount to be paid if Jessica borrowed a sum of $5750 at 7% simple interest for 8 years.

(5) Calculate the amount due if Karen borrowed a sum of $3950 at 4% simple interest for 4 years.

(6) In how much time a principal of $3200 will amount to $3680 at a simple interest of 5% per annum?

(7) What amount does David have to pay after 6 years if he takes a loan of $3400 at 3% simple interest?

(8) In how much time a principal of $3200 will amount to $3456 at a simple interest of 4% per annum?

(9) If Jennifer paid $3900 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(10) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $12600 to clear the loan, then find the time period of the loan.


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