Question:
If Paul paid $5640 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
Correct Answer
$4700
Solution And Explanation
Solution
Given,
Amount (A) = $5640
Rate of Simple Interest (R) = 5%
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
$5640 = P (1 + 5% × 4)
⇒ $5640 = P (1 + 5/100 × 4)
⇒ $5640 = P (1 + 5 × 4/100)
⇒ $5640 = P (1 + 20/100)
⇒ $5640 = P (100 + 20/100)
⇒ $5640 = P × 120/100
⇒ P × 120/100 = $5640
⇒ P = 5640/120/100
⇒ P = 5640 × 100/120
⇒ P = 5640 × 100/120
⇒ P = 564000/120
⇒ P = $4700
Thus, the sum borrowed (P) = $4700 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 = 5% per annum
Thus, Interest = 5% of principal
⇒ Interest = 5% of 100 = 5
Thus, Simple Interest for 1 year = 5
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 × 5 = 20
Thus, simple interest for 4 years = 20
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 20 = 120
Calculation of the Principal
Now,
∵ If the Amount is 120, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/120
∴ If the Amount is 5640, then the Principal = 100/120 × 5640
= 100 × 5640/120
= 564000/120
= 4700
Thus, Principal = $4700
Thus, the sum borrowed = $4700 Answer
Similar Questions
(1) In how much time a principal of $3150 will amount to $3528 at a simple interest of 4% per annum?
(2) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 4% simple interest?
(3) Calculate the amount due if Karen borrowed a sum of $3950 at 9% simple interest for 3 years.
(4) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $8965 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Jessica borrowed a sum of $5750 at 5% simple interest for 8 years.
(6) In how much time a principal of $3150 will amount to $3654 at a simple interest of 4% per annum?
(7) Find the amount to be paid if Sarah borrowed a sum of $5850 at 10% simple interest for 7 years.
(8) Calculate the amount due if David borrowed a sum of $3400 at 10% simple interest for 4 years.
(9) Calculate the amount due if Barbara borrowed a sum of $3550 at 4% simple interest for 3 years.
(10) How much loan did Sharon borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8525 to clear it?