Question:
If Patricia paid $3780 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
Correct Answer
$3150
Solution And Explanation
Solution
Given,
Amount (A) = $3780
Rate of Simple Interest (R) = 5%
Time (T) = 4 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
$3780 = P (1 + 5% × 4)
⇒ $3780 = P (1 + 5/100 × 4)
⇒ $3780 = P (1 + 5 × 4/100)
⇒ $3780 = P (1 + 20/100)
⇒ $3780 = P (100 + 20/100)
⇒ $3780 = P × 120/100
⇒ P × 120/100 = $3780
⇒ P = 3780/120/100
⇒ P = 3780 × 100/120
⇒ P = 3780 × 100/120
⇒ P = 378000/120
⇒ P = $3150
Thus, the sum borrowed (P) = $3150 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 = 5% per annum
Thus, Interest = 5% of principal
⇒ Interest = 5% of 100 = 5
Thus, Simple Interest for 1 year = 5
Calculation of the Amount
Since, in the question, time = 4 years
So, we need to calculate the simple interest for the given time period, which is 4 years
Thus, Simple Interest for 4 years = 4 × Simple Interest for 1 year
= 4 × 5 = 20
Thus, simple interest for 4 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 3780, then the Principal = 100/120 × 3780
= 100 × 3780/120
= 378000/120
= 3150
Thus, Principal = $3150
Thus, the sum borrowed = $3150 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 8% simple interest.
(2) Calculate the amount due if James borrowed a sum of $3000 at 4% simple interest for 4 years.
(3) If Joshua paid $5880 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(4) Calculate the amount due if James borrowed a sum of $3000 at 5% simple interest for 4 years.
(5) Find the amount to be paid if Karen borrowed a sum of $5950 at 9% simple interest for 7 years.
(6) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 9% simple interest.
(7) Calculate the amount due if Richard borrowed a sum of $3600 at 7% simple interest for 3 years.
(8) How much loan did Ryan borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9875 to clear it?
(9) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 8% simple interest.
(10) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 9% simple interest for 4 years.