Simple Interest
MCQs Math


Question:     If Patricia paid $3654 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.


Correct Answer  $3150

Solution And Explanation

Solution

Given,

Amount (A) = $3654

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

$3654 = P (1 + 4% × 4)

⇒ $3654 = P (1 + 4/100 × 4)

⇒ $3654 = P (1 + 4 × 4/100)

⇒ $3654 = P (1 + 16/100)

⇒ $3654 = P (100 + 16/100)

⇒ $3654 = P × 116/100

⇒ P × 116/100 = $3654

⇒ P = 3654/116/100

⇒ P = 3654 × 100/116

⇒ P = 3654 × 100/116

⇒ P = 365400/116

⇒ P = $3150

Thus, the sum borrowed (P) = $3150 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 3654, then the Principal = 100/116 × 3654

= 100 × 3654/116

= 365400/116

= 3150

Thus, Principal = $3150

Thus, the sum borrowed = $3150 Answer


Similar Questions

(1) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 8% simple interest?

(2) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 10% simple interest?

(3) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 3% simple interest?

(4) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 9% simple interest?

(5) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 5% simple interest?

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

(7) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 5% simple interest.

(8) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 4% simple interest?

(9) Calculate the amount due if James borrowed a sum of $3000 at 8% simple interest for 4 years.

(10) Find the amount to be paid if Barbara borrowed a sum of $5550 at 9% simple interest for 8 years.


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