Question:
Christopher had to pay $4240 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
Correct Answer
$4000
Solution And Explanation
Solution
Given,
Amount (A) = $4240
Rate of Simple Interest (R) = 2%
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
$4240 = P (1 + 2% × 3)
⇒ $4240 = P (1 + 2/100 × 3)
⇒ $4240 = P (1 + 2 × 3/100)
⇒ $4240 = P (1 + 6/100)
⇒ $4240 = P (100 + 6/100)
⇒ $4240 = P × 106/100
⇒ P × 106/100 = $4240
⇒ P = 4240/106/100
⇒ P = 4240 × 100/106
⇒ P = 4240 × 100/106
⇒ P = 424000/106
⇒ P = $4000
Thus, the sum borrowed (P) = $4000 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 = 2% per annum
Thus, Interest = 2% of principal
⇒ Interest = 2% of 100 = 2
Thus, Simple Interest for 1 year = 2
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 × 2 = 6
Thus, simple interest for 3 years = 6
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 6 = 106
Calculation of the Principal
Now,
∵ If the Amount is 106, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/106
∴ If the Amount is 4240, then the Principal = 100/106 × 4240
= 100 × 4240/106
= 424000/106
= 4000
Thus, Principal = $4000
Thus, the sum borrowed = $4000 Answer
Similar Questions
(1) Find the amount to be paid if Sarah borrowed a sum of $5850 at 3% simple interest for 7 years.
(2) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 5% simple interest?
(3) How much loan did Joshua borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7935 to clear it?
(4) If Linda paid $4020 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(5) Calculate the amount due if Christopher borrowed a sum of $4000 at 9% simple interest for 4 years.
(6) Calculate the amount due if Patricia borrowed a sum of $3150 at 8% simple interest for 4 years.
(7) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 2% simple interest.
(8) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 2% simple interest.
(9) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $7310 to clear the loan, then find the time period of the loan.
(10) Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $11696 to clear the loan, then find the time period of the loan.