Question:
How much loan did Elizabeth borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6267.5 to clear it?
Correct Answer
$5450
Solution And Explanation
Solution
Given,
Amount (A) = $6267.5
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
$6267.5 = P (1 + 3% × 5)
⇒ $6267.5 = P (1 + 3/100 × 5)
⇒ $6267.5 = P (1 + 3 × 5/100)
⇒ $6267.5 = P (1 + 15/100)
⇒ $6267.5 = P (100 + 15/100)
⇒ $6267.5 = P × 115/100
⇒ P × 115/100 = $6267.5
⇒ P = 6267.5/115/100
⇒ P = 6267.5 × 100/115
⇒ P = 6267.5 × 100/115
⇒ P = 626750/115
⇒ P = $5450
Thus, the sum borrowed (P) = $5450 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 6267.5, then the Principal = 100/115 × 6267.5
= 100 × 6267.5/115
= 626750/115
= 5450
Thus, Principal = $5450
Thus, the sum borrowed = $5450 Answer
Similar Questions
(1) Find the amount to be paid if John borrowed a sum of $5200 at 6% simple interest for 8 years.
(2) If Joshua paid $5880 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(3) Calculate the amount due if Michael borrowed a sum of $3300 at 5% simple interest for 4 years.
(4) How much loan did Patricia borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6180 to clear it?
(5) If Andrew paid $5376 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(6) In how much time a principal of $3050 will amount to $3507.5 at a simple interest of 3% per annum?
(7) Calculate the amount due if Jennifer borrowed a sum of $3250 at 9% simple interest for 4 years.
(8) Find the amount to be paid if Karen borrowed a sum of $5950 at 5% simple interest for 7 years.
(9) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $8280 to clear the loan, then find the time period of the loan.
(10) How much loan did Jason borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8470 to clear it?