Question:
How much loan did Anthony borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7875 to clear it?
Correct Answer
$6300
Solution And Explanation
Solution
Given,
Amount (A) = $7875
Rate of Simple Interest (R) = 5%
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
$7875 = P (1 + 5% × 5)
⇒ $7875 = P (1 + 5/100 × 5)
⇒ $7875 = P (1 + 5 × 5/100)
⇒ $7875 = P (1 + 25/100)
⇒ $7875 = P (100 + 25/100)
⇒ $7875 = P × 125/100
⇒ P × 125/100 = $7875
⇒ P = 7875/125/100
⇒ P = 7875 × 100/125
⇒ P = 7875 × 100/125
⇒ P = 787500/125
⇒ 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 = 5% per annum
Thus, Interest = 5% of principal
⇒ Interest = 5% of 100 = 5
Thus, Simple Interest for 1 year = 5
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 × 5 = 25
Thus, simple interest for 5 years = 25
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 25 = 125
Calculation of the Principal
Now,
∵ If the Amount is 125, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/125
∴ If the Amount is 7875, then the Principal = 100/125 × 7875
= 100 × 7875/125
= 787500/125
= 6300
Thus, Principal = $6300
Thus, the sum borrowed = $6300 Answer
Similar Questions
(1) Calculate the amount due if Karen borrowed a sum of $3950 at 4% simple interest for 3 years.
(2) If Elizabeth paid $3726 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(3) In how much time a principal of $3200 will amount to $3712 at a simple interest of 4% per annum?
(4) Calculate the amount due if John borrowed a sum of $3200 at 4% simple interest for 4 years.
(5) Calculate the amount due if Robert borrowed a sum of $3100 at 9% simple interest for 3 years.
(6) Barbara had to pay $3976 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(7) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 6% simple interest?
(8) How much loan did Nancy borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6765 to clear it?
(9) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 8% simple interest.
(10) Calculate the amount due if William borrowed a sum of $3500 at 5% simple interest for 3 years.