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) If Linda paid $3886 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(2) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $8084 to clear the loan, then find the time period of the loan.
(3) If Margaret paid $5220 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 Jennifer borrowed a sum of $5250 at a rate of 2% simple interest.
(5) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 3% simple interest.
(6) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 9% simple interest?
(7) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $10400 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 5% simple interest.
(9) Jennifer took a loan of $4500 at the rate of 10% simple interest per annum. If he paid an amount of $9000 to clear the loan, then find the time period of the loan.
(10) In how much time a principal of $3150 will amount to $3528 at a simple interest of 4% per annum?