Question:
How much loan did Patricia borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5665 to clear it?
Correct Answer
$5150
Solution And Explanation
Solution
Given,
Amount (A) = $5665
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
$5665 = P (1 + 2% × 5)
⇒ $5665 = P (1 + 2/100 × 5)
⇒ $5665 = P (1 + 2 × 5/100)
⇒ $5665 = P (1 + 10/100)
⇒ $5665 = P (100 + 10/100)
⇒ $5665 = P × 110/100
⇒ P × 110/100 = $5665
⇒ P = 5665/110/100
⇒ P = 5665 × 100/110
⇒ P = 5665 × 100/110
⇒ P = 566500/110
⇒ P = $5150
Thus, the sum borrowed (P) = $5150 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 5665, then the Principal = 100/110 × 5665
= 100 × 5665/110
= 566500/110
= 5150
Thus, Principal = $5150
Thus, the sum borrowed = $5150 Answer
Similar Questions
(1) Lisa had to pay $4414.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(2) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 10% simple interest.
(3) Andrew had to pay $5376 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(4) How much loan did Mary borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6060 to clear it?
(5) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 4% simple interest.
(6) Calculate the amount due if Sarah borrowed a sum of $3850 at 7% simple interest for 4 years.
(7) If Matthew paid $4872 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(8) Susan had to pay $3978.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(9) Find the amount to be paid if Christopher borrowed a sum of $6000 at 8% simple interest for 7 years.
(10) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $8288 to clear the loan, then find the time period of the loan.