Question:
If Joshua paid $5684 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
Correct Answer
$4900
Solution And Explanation
Solution
Given,
Amount (A) = $5684
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
$5684 = P (1 + 4% × 4)
⇒ $5684 = P (1 + 4/100 × 4)
⇒ $5684 = P (1 + 4 × 4/100)
⇒ $5684 = P (1 + 16/100)
⇒ $5684 = P (100 + 16/100)
⇒ $5684 = P × 116/100
⇒ P × 116/100 = $5684
⇒ P = 5684/116/100
⇒ P = 5684 × 100/116
⇒ P = 5684 × 100/116
⇒ P = 568400/116
⇒ P = $4900
Thus, the sum borrowed (P) = $4900 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 5684, then the Principal = 100/116 × 5684
= 100 × 5684/116
= 568400/116
= 4900
Thus, Principal = $4900
Thus, the sum borrowed = $4900 Answer
Similar Questions
(1) Calculate the amount due if Richard borrowed a sum of $3600 at 8% simple interest for 3 years.
(2) Find the amount to be paid if Joseph borrowed a sum of $5700 at 3% simple interest for 7 years.
(3) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $7176 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 9% simple interest.
(5) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $5680 to clear the loan, then find the time period of the loan.
(6) In how much time a principal of $3150 will amount to $3780 at a simple interest of 5% per annum?
(7) Find the amount to be paid if William borrowed a sum of $5500 at 10% simple interest for 8 years.
(8) Find the amount to be paid if Richard borrowed a sum of $5600 at 3% simple interest for 7 years.
(9) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $12040 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 4% simple interest.