Question:
If Charles paid $4524 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
Correct Answer
$3900
Solution And Explanation
Solution
Given,
Amount (A) = $4524
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
$4524 = P (1 + 4% × 4)
⇒ $4524 = P (1 + 4/100 × 4)
⇒ $4524 = P (1 + 4 × 4/100)
⇒ $4524 = P (1 + 16/100)
⇒ $4524 = P (100 + 16/100)
⇒ $4524 = P × 116/100
⇒ P × 116/100 = $4524
⇒ P = 4524/116/100
⇒ P = 4524 × 100/116
⇒ P = 4524 × 100/116
⇒ P = 452400/116
⇒ 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 = 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 4524, then the Principal = 100/116 × 4524
= 100 × 4524/116
= 452400/116
= 3900
Thus, Principal = $3900
Thus, the sum borrowed = $3900 Answer
Similar Questions
(1) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $11340 to clear the loan, then find the time period of the loan.
(2) How much loan did Steven borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8250 to clear it?
(3) Calculate the amount due if John borrowed a sum of $3200 at 9% simple interest for 4 years.
(4) Michael had to pay $3795 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(5) Calculate the amount due if Barbara borrowed a sum of $3550 at 5% simple interest for 3 years.
(6) How much loan did Kenneth borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8400 to clear it?
(7) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 4% simple interest.
(8) How much loan did Charles borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7080 to clear it?
(9) Find the amount to be paid if Charles borrowed a sum of $5900 at 5% simple interest for 7 years.
(10) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $10296 to clear the loan, then find the time period of the loan.