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 10 years if Elizabeth borrowed a sum of $5450 at a rate of 6% simple interest.
(2) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $7897 to clear the loan, then find the time period of the loan.
(3) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $7072 to clear the loan, then find the time period of the loan.
(4) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 4% simple interest?
(5) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 8% simple interest.
(6) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $8732 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 2% simple interest.
(8) Elizabeth had to pay $3657 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(9) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $11590 to clear the loan, then find the time period of the loan.
(10) How much loan did Betty borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6875 to clear it?