Question:
How much loan did Joseph borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6270 to clear it?
Correct Answer
$5700
Solution And Explanation
Solution
Given,
Amount (A) = $6270
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
$6270 = P (1 + 2% × 5)
⇒ $6270 = P (1 + 2/100 × 5)
⇒ $6270 = P (1 + 2 × 5/100)
⇒ $6270 = P (1 + 10/100)
⇒ $6270 = P (100 + 10/100)
⇒ $6270 = P × 110/100
⇒ P × 110/100 = $6270
⇒ P = 6270/110/100
⇒ P = 6270 × 100/110
⇒ P = 6270 × 100/110
⇒ P = 627000/110
⇒ P = $5700
Thus, the sum borrowed (P) = $5700 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 6270, then the Principal = 100/110 × 6270
= 100 × 6270/110
= 627000/110
= 5700
Thus, Principal = $5700
Thus, the sum borrowed = $5700 Answer
Similar Questions
(1) If William borrowed $3500 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(2) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $6800 to clear the loan, then find the time period of the loan.
(3) How much loan did David borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6480 to clear it?
(4) How much loan did Mary borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6060 to clear it?
(5) Calculate the amount due if Robert borrowed a sum of $3100 at 8% simple interest for 4 years.
(6) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $7526 to clear the loan, then find the time period of the loan.
(7) In how much time a principal of $3150 will amount to $3780 at a simple interest of 5% per annum?
(8) Calculate the amount due if Thomas borrowed a sum of $3800 at 9% simple interest for 3 years.
(9) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $5680 to clear the loan, then find the time period of the loan.
(10) Kimberly had to pay $4929 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.