Question:
How much loan did Laura borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8635 to clear it?
Correct Answer
$7850
Solution And Explanation
Solution
Given,
Amount (A) = $8635
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
$8635 = P (1 + 2% × 5)
⇒ $8635 = P (1 + 2/100 × 5)
⇒ $8635 = P (1 + 2 × 5/100)
⇒ $8635 = P (1 + 10/100)
⇒ $8635 = P (100 + 10/100)
⇒ $8635 = P × 110/100
⇒ P × 110/100 = $8635
⇒ P = 8635/110/100
⇒ P = 8635 × 100/110
⇒ P = 8635 × 100/110
⇒ P = 863500/110
⇒ P = $7850
Thus, the sum borrowed (P) = $7850 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 8635, then the Principal = 100/110 × 8635
= 100 × 8635/110
= 863500/110
= 7850
Thus, Principal = $7850
Thus, the sum borrowed = $7850 Answer
Similar Questions
(1) If Joshua paid $5684 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(2) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 8% simple interest.
(3) Calculate the amount due if Charles borrowed a sum of $3900 at 9% simple interest for 4 years.
(4) How much loan did John borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6240 to clear it?
(5) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 8% simple interest.
(6) Find the amount to be paid if Joseph borrowed a sum of $5700 at 2% simple interest for 8 years.
(7) Calculate the amount due if William borrowed a sum of $3500 at 2% simple interest for 4 years.
(8) How much loan did Sandra borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7740 to clear it?
(9) Calculate the amount due if Michael borrowed a sum of $3300 at 7% simple interest for 4 years.
(10) Calculate the amount due if Jennifer borrowed a sum of $3250 at 3% simple interest for 4 years.