Question:
How much loan did Patricia borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6180 to clear it?
Correct Answer
$5150
Solution And Explanation
Solution
Given,
Amount (A) = $6180
Rate of Simple Interest (R) = 4%
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
$6180 = P (1 + 4% × 5)
⇒ $6180 = P (1 + 4/100 × 5)
⇒ $6180 = P (1 + 4 × 5/100)
⇒ $6180 = P (1 + 20/100)
⇒ $6180 = P (100 + 20/100)
⇒ $6180 = P × 120/100
⇒ P × 120/100 = $6180
⇒ P = 6180/120/100
⇒ P = 6180 × 100/120
⇒ P = 6180 × 100/120
⇒ P = 618000/120
⇒ 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 = 4% per annum
Thus, Interest = 4% of principal
⇒ Interest = 4% of 100 = 4
Thus, Simple Interest for 1 year = 4
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 × 4 = 20
Thus, simple interest for 5 years = 20
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 20 = 120
Calculation of the Principal
Now,
∵ If the Amount is 120, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/120
∴ If the Amount is 6180, then the Principal = 100/120 × 6180
= 100 × 6180/120
= 618000/120
= 5150
Thus, Principal = $5150
Thus, the sum borrowed = $5150 Answer
Similar Questions
(1) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 6% simple interest for 8 years.
(2) Find the amount to be paid if Barbara borrowed a sum of $5550 at 2% simple interest for 7 years.
(3) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $10212 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if Christopher borrowed a sum of $4000 at 7% simple interest for 3 years.
(5) Calculate the amount due if Mary borrowed a sum of $3050 at 2% simple interest for 4 years.
(6) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 4% simple interest?
(7) If Andrew paid $5184 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(8) If Anthony paid $4644 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(9) Calculate the amount due if Jessica borrowed a sum of $3750 at 3% simple interest for 3 years.
(10) Calculate the amount due if Charles borrowed a sum of $3900 at 5% simple interest for 3 years.