Question:
If Joseph paid $4292 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
Correct Answer
$3700
Solution And Explanation
Solution
Given,
Amount (A) = $4292
Rate of Simple Interest (R) = 4%
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
$4292 = P (1 + 4% × 4)
⇒ $4292 = P (1 + 4/100 × 4)
⇒ $4292 = P (1 + 4 × 4/100)
⇒ $4292 = P (1 + 16/100)
⇒ $4292 = P (100 + 16/100)
⇒ $4292 = P × 116/100
⇒ P × 116/100 = $4292
⇒ P = 4292/116/100
⇒ P = 4292 × 100/116
⇒ P = 4292 × 100/116
⇒ P = 429200/116
⇒ P = $3700
Thus, the sum borrowed (P) = $3700 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 = 4% per annum
Thus, Interest = 4% of principal
⇒ Interest = 4% of 100 = 4
Thus, Simple Interest for 1 year = 4
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 × 4 = 16
Thus, simple interest for 4 years = 16
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 16 = 116
Calculation of the Principal
Now,
∵ If the Amount is 116, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/116
∴ If the Amount is 4292, then the Principal = 100/116 × 4292
= 100 × 4292/116
= 429200/116
= 3700
Thus, Principal = $3700
Thus, the sum borrowed = $3700 Answer
Similar Questions
(1) How much loan did Joshua borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7590 to clear it?
(2) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 6% simple interest.
(3) How much loan did Mark borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8000 to clear it?
(4) What amount does David have to pay after 5 years if he takes a loan of $3400 at 4% simple interest?
(5) Susan had to pay $4088 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(6) How much loan did Donna borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7535 to clear it?
(7) Calculate the amount due if James borrowed a sum of $3000 at 8% simple interest for 4 years.
(8) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $9685 to clear the loan, then find the time period of the loan.
(9) How much loan did Brian borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9000 to clear it?
(10) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 9% simple interest.