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) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 5% simple interest?
(2) In how much time a principal of $3150 will amount to $3339 at a simple interest of 2% per annum?
(3) Calculate the amount due if Christopher borrowed a sum of $4000 at 4% simple interest for 3 years.
(4) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $9500 to clear the loan, then find the time period of the loan.
(5) Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $9940 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 5% simple interest.
(7) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 8% simple interest.
(8) Calculate the amount due if Mary borrowed a sum of $3050 at 9% simple interest for 4 years.
(9) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $10664 to clear the loan, then find the time period of the loan.
(10) How much loan did Joseph borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7125 to clear it?