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) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 6% simple interest.
(2) If Patricia paid $3780 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(3) In how much time a principal of $3200 will amount to $3520 at a simple interest of 5% per annum?
(4) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 9% simple interest.
(5) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $9372 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if Linda borrowed a sum of $3350 at 10% simple interest for 4 years.
(7) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $10400 to clear the loan, then find the time period of the loan.
(8) If Donald paid $4860 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(9) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 9% simple interest?
(10) How much loan did Rebecca borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9562.5 to clear it?