Question:
How much loan did Carol borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8107.5 to clear it?
Correct Answer
$7050
Solution And Explanation
Solution
Given,
Amount (A) = $8107.5
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
$8107.5 = P (1 + 3% × 5)
⇒ $8107.5 = P (1 + 3/100 × 5)
⇒ $8107.5 = P (1 + 3 × 5/100)
⇒ $8107.5 = P (1 + 15/100)
⇒ $8107.5 = P (100 + 15/100)
⇒ $8107.5 = P × 115/100
⇒ P × 115/100 = $8107.5
⇒ P = 8107.5/115/100
⇒ P = 8107.5 × 100/115
⇒ P = 8107.5 × 100/115
⇒ P = 810750/115
⇒ P = $7050
Thus, the sum borrowed (P) = $7050 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 8107.5, then the Principal = 100/115 × 8107.5
= 100 × 8107.5/115
= 810750/115
= 7050
Thus, Principal = $7050
Thus, the sum borrowed = $7050 Answer
Similar Questions
(1) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 3% simple interest?
(2) In how much time a principal of $3000 will amount to $3120 at a simple interest of 2% per annum?
(3) How much loan did Jacob borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9200 to clear it?
(4) What amount will be due after 2 years if John borrowed a sum of $3100 at a 9% simple interest?
(5) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $10080 to clear the loan, then find the time period of the loan.
(6) 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?
(7) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 6% simple interest.
(8) If Karen paid $4582 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(9) Calculate the amount due if Patricia borrowed a sum of $3150 at 5% simple interest for 4 years.
(10) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 6% simple interest?