Question:
How much loan did Anthony borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7245 to clear it?
Correct Answer
$6300
Solution And Explanation
Solution
Given,
Amount (A) = $7245
Rate of Simple Interest (R) = 3%
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
$7245 = P (1 + 3% × 5)
⇒ $7245 = P (1 + 3/100 × 5)
⇒ $7245 = P (1 + 3 × 5/100)
⇒ $7245 = P (1 + 15/100)
⇒ $7245 = P (100 + 15/100)
⇒ $7245 = P × 115/100
⇒ P × 115/100 = $7245
⇒ P = 7245/115/100
⇒ P = 7245 × 100/115
⇒ P = 7245 × 100/115
⇒ P = 724500/115
⇒ P = $6300
Thus, the sum borrowed (P) = $6300 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 = 3% per annum
Thus, Interest = 3% of principal
⇒ Interest = 3% of 100 = 3
Thus, Simple Interest for 1 year = 3
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 × 3 = 15
Thus, simple interest for 5 years = 15
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 15 = 115
Calculation of the Principal
Now,
∵ If the Amount is 115, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/115
∴ If the Amount is 7245, then the Principal = 100/115 × 7245
= 100 × 7245/115
= 724500/115
= 6300
Thus, Principal = $6300
Thus, the sum borrowed = $6300 Answer
Similar Questions
(1) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 10% simple interest?
(2) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $11020 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Sarah borrowed a sum of $5850 at 9% simple interest for 7 years.
(4) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $6216 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Thomas borrowed a sum of $5800 at 2% simple interest for 7 years.
(6) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $11008 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if James borrowed a sum of $3000 at 7% simple interest for 4 years.
(8) How much loan did Patricia borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5665 to clear it?
(9) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 6% simple interest?
(10) If Betty paid $4590 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.