Question:
If James paid $3240 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
Correct Answer
$3000
Solution And Explanation
Solution
Given,
Amount (A) = $3240
Rate of Simple Interest (R) = 2%
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
$3240 = P (1 + 2% × 4)
⇒ $3240 = P (1 + 2/100 × 4)
⇒ $3240 = P (1 + 2 × 4/100)
⇒ $3240 = P (1 + 8/100)
⇒ $3240 = P (100 + 8/100)
⇒ $3240 = P × 108/100
⇒ P × 108/100 = $3240
⇒ P = 3240/108/100
⇒ P = 3240 × 100/108
⇒ P = 3240 × 100/108
⇒ P = 324000/108
⇒ P = $3000
Thus, the sum borrowed (P) = $3000 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 = 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 × 2 = 8
Thus, simple interest for 4 years = 8
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 8 = 108
Calculation of the Principal
Now,
∵ If the Amount is 108, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/108
∴ If the Amount is 3240, then the Principal = 100/108 × 3240
= 100 × 3240/108
= 324000/108
= 3000
Thus, Principal = $3000
Thus, the sum borrowed = $3000 Answer
Similar Questions
(1) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 2% simple interest for 8 years.
(2) Nancy had to pay $4399 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(3) How much loan did Timothy borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8140 to clear it?
(4) In how much time a principal of $3150 will amount to $3433.5 at a simple interest of 3% per annum?
(5) Find the amount to be paid if James borrowed a sum of $5000 at 6% simple interest for 8 years.
(6) Calculate the amount due if Michael borrowed a sum of $3300 at 5% simple interest for 3 years.
(7) Find the amount to be paid if Barbara borrowed a sum of $5550 at 3% simple interest for 7 years.
(8) Find the amount to be paid if Jessica borrowed a sum of $5750 at 2% simple interest for 8 years.
(9) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $7310 to clear the loan, then find the time period of the loan.
(10) If Donald paid $5220 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.