Question:
Patricia had to pay $3622.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
Correct Answer
$3150
Solution And Explanation
Solution
Given,
Amount (A) = $3622.5
Rate of Simple Interest (R) = 5%
Time (T) = 3 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
$3622.5 = P (1 + 5% × 3)
⇒ $3622.5 = P (1 + 5/100 × 3)
⇒ $3622.5 = P (1 + 5 × 3/100)
⇒ $3622.5 = P (1 + 15/100)
⇒ $3622.5 = P (100 + 15/100)
⇒ $3622.5 = P × 115/100
⇒ P × 115/100 = $3622.5
⇒ P = 3622.5/115/100
⇒ P = 3622.5 × 100/115
⇒ P = 3622.5 × 100/115
⇒ P = 362250/115
⇒ 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 = 3 years
So, we need to calculate the simple interest for the given time period, which is 3 years
Thus, Simple Interest for 3 years = 3 × Simple Interest for 1 year
= 3 × 5 = 15
Thus, simple interest for 3 years = 15
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 15 = 115
Calculation of the Principal
Now,
∵ If the Amount is 115, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/115
∴ If the Amount is 3622.5, then the Principal = 100/115 × 3622.5
= 100 × 3622.5/115
= 362250/115
= 3150
Thus, Principal = $3150
Thus, the sum borrowed = $3150 Answer
Similar Questions
(1) If Kimberly paid $5394 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(2) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $9600 to clear the loan, then find the time period of the loan.
(3) If Richard paid $4320 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 after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 6% simple interest.
(5) What amount does John have to pay after 5 years if he takes a loan of $3200 at 3% simple interest?
(6) Find the amount to be paid if Thomas borrowed a sum of $5800 at 6% simple interest for 7 years.
(7) In how much time a principal of $3100 will amount to $3875 at a simple interest of 5% per annum?
(8) Calculate the amount due if Linda borrowed a sum of $3350 at 8% simple interest for 3 years.
(9) In how much time a principal of $3050 will amount to $3172 at a simple interest of 2% per annum?
(10) Find the amount to be paid if Jessica borrowed a sum of $5750 at 8% simple interest for 8 years.