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) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $7380 to clear the loan, then find the time period of the loan.
(2) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $7242 to clear the loan, then find the time period of the loan.
(3) If Robert paid $3348 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(4) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 3% simple interest?
(5) Find the amount to be paid if Michael borrowed a sum of $5300 at 2% simple interest for 7 years.
(6) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $8507 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if Jessica borrowed a sum of $3750 at 7% simple interest for 3 years.
(8) Find the amount to be paid if William borrowed a sum of $5500 at 7% simple interest for 7 years.
(9) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 5% simple interest?
(10) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $7992 to clear the loan, then find the time period of the loan.