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) How much loan did Richard borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6720 to clear it?
(2) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 10% simple interest.
(3) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 6% simple interest for 8 years.
(4) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 4% simple interest.
(5) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 5% simple interest?
(6) In how much time a principal of $3000 will amount to $3240 at a simple interest of 2% per annum?
(7) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 2% simple interest.
(8) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 5% simple interest.
(9) Find the amount to be paid if Charles borrowed a sum of $5900 at 7% simple interest for 8 years.
(10) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $10560 to clear the loan, then find the time period of the loan.