Question:
How much loan did John borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5720 to clear it?
Correct Answer
$5200
Solution And Explanation
Solution
Given,
Amount (A) = $5720
Rate of Simple Interest (R) = 2%
Time (T) = 5 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
$5720 = P (1 + 2% × 5)
⇒ $5720 = P (1 + 2/100 × 5)
⇒ $5720 = P (1 + 2 × 5/100)
⇒ $5720 = P (1 + 10/100)
⇒ $5720 = P (100 + 10/100)
⇒ $5720 = P × 110/100
⇒ P × 110/100 = $5720
⇒ P = 5720/110/100
⇒ P = 5720 × 100/110
⇒ P = 5720 × 100/110
⇒ P = 572000/110
⇒ P = $5200
Thus, the sum borrowed (P) = $5200 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 = 2% per annum
Thus, Interest = 2% of principal
⇒ Interest = 2% of 100 = 2
Thus, Simple Interest for 1 year = 2
Calculation of the Amount
Since, in the question, time = 5 years
So, we need to calculate the simple interest for the given time period, which is 5 years
Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year
= 5 × 2 = 10
Thus, simple interest for 5 years = 10
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 10 = 110
Calculation of the Principal
Now,
∵ If the Amount is 110, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/110
∴ If the Amount is 5720, then the Principal = 100/110 × 5720
= 100 × 5720/110
= 572000/110
= 5200
Thus, Principal = $5200
Thus, the sum borrowed = $5200 Answer
Similar Questions
(1) Find the amount to be paid if Linda borrowed a sum of $5350 at 6% simple interest for 7 years.
(2) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $9840 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Thomas borrowed a sum of $5800 at 4% simple interest for 8 years.
(4) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 6% simple interest.
(5) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $12127 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Michael borrowed a sum of $5300 at 10% simple interest for 7 years.
(7) If Matthew paid $5040 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(8) In how much time a principal of $3000 will amount to $3600 at a simple interest of 5% per annum?
(9) Find the amount to be paid if John borrowed a sum of $5200 at 10% simple interest for 8 years.
(10) Find the amount to be paid if Joseph borrowed a sum of $5700 at 7% simple interest for 8 years.