Question:
How much loan did Amanda borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7865 to clear it?
Correct Answer
$7150
Solution And Explanation
Solution
Given,
Amount (A) = $7865
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
$7865 = P (1 + 2% × 5)
⇒ $7865 = P (1 + 2/100 × 5)
⇒ $7865 = P (1 + 2 × 5/100)
⇒ $7865 = P (1 + 10/100)
⇒ $7865 = P (100 + 10/100)
⇒ $7865 = P × 110/100
⇒ P × 110/100 = $7865
⇒ P = 7865/110/100
⇒ P = 7865 × 100/110
⇒ P = 7865 × 100/110
⇒ P = 786500/110
⇒ P = $7150
Thus, the sum borrowed (P) = $7150 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 7865, then the Principal = 100/110 × 7865
= 100 × 7865/110
= 786500/110
= 7150
Thus, Principal = $7150
Thus, the sum borrowed = $7150 Answer
Similar Questions
(1) Calculate the amount due if Richard borrowed a sum of $3600 at 10% simple interest for 4 years.
(2) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $7526 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 4% simple interest.
(4) If Michael paid $3564 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(5) Calculate the amount due if Patricia borrowed a sum of $3150 at 4% simple interest for 4 years.
(6) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $9600 to clear the loan, then find the time period of the loan.
(7) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $8820 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Thomas borrowed a sum of $5800 at 5% simple interest for 7 years.
(9) If Anthony paid $5160 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(10) Calculate the amount due if Christopher borrowed a sum of $4000 at 2% simple interest for 4 years.