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) Calculate the amount due if Susan borrowed a sum of $3650 at 4% simple interest for 3 years.
(2) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $9880 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if William borrowed a sum of $5500 at 4% simple interest for 7 years.
(4) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $6256 to clear the loan, then find the time period of the loan.
(5) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $8000 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 8% simple interest.
(7) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 9% simple interest.
(8) If Matthew paid $4704 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(9) How much loan did Sharon borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8525 to clear it?
(10) Calculate the amount due if James borrowed a sum of $3000 at 6% simple interest for 4 years.