Question:
Karen had to pay $4305.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
Correct Answer
$3950
Solution And Explanation
Solution
Given,
Amount (A) = $4305.5
Rate of Simple Interest (R) = 3%
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
$4305.5 = P (1 + 3% × 3)
⇒ $4305.5 = P (1 + 3/100 × 3)
⇒ $4305.5 = P (1 + 3 × 3/100)
⇒ $4305.5 = P (1 + 9/100)
⇒ $4305.5 = P (100 + 9/100)
⇒ $4305.5 = P × 109/100
⇒ P × 109/100 = $4305.5
⇒ P = 4305.5/109/100
⇒ P = 4305.5 × 100/109
⇒ P = 4305.5 × 100/109
⇒ P = 430550/109
⇒ P = $3950
Thus, the sum borrowed (P) = $3950 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 = 3% per annum
Thus, Interest = 3% of principal
⇒ Interest = 3% of 100 = 3
Thus, Simple Interest for 1 year = 3
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 × 3 = 9
Thus, simple interest for 3 years = 9
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 9 = 109
Calculation of the Principal
Now,
∵ If the Amount is 109, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/109
∴ If the Amount is 4305.5, then the Principal = 100/109 × 4305.5
= 100 × 4305.5/109
= 430550/109
= 3950
Thus, Principal = $3950
Thus, the sum borrowed = $3950 Answer
Similar Questions
(1) If Lisa paid $4860 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(2) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $12600 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Barbara borrowed a sum of $3550 at 9% simple interest for 3 years.
(4) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 6% simple interest.
(5) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 5% simple interest?
(6) Find the amount to be paid if John borrowed a sum of $5200 at 4% simple interest for 8 years.
(7) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $6068 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 4% simple interest for 8 years.
(9) How much loan did Rebecca borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8415 to clear it?
(10) Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $8584 to clear the loan, then find the time period of the loan.