Question:
If William paid $4060 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
Correct Answer
$3500
Solution And Explanation
Solution
Given,
Amount (A) = $4060
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
$4060 = P (1 + 4% × 4)
⇒ $4060 = P (1 + 4/100 × 4)
⇒ $4060 = P (1 + 4 × 4/100)
⇒ $4060 = P (1 + 16/100)
⇒ $4060 = P (100 + 16/100)
⇒ $4060 = P × 116/100
⇒ P × 116/100 = $4060
⇒ P = 4060/116/100
⇒ P = 4060 × 100/116
⇒ P = 4060 × 100/116
⇒ P = 406000/116
⇒ P = $3500
Thus, the sum borrowed (P) = $3500 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 4060, then the Principal = 100/116 × 4060
= 100 × 4060/116
= 406000/116
= 3500
Thus, Principal = $3500
Thus, the sum borrowed = $3500 Answer
Similar Questions
(1) Calculate the amount due if Jennifer borrowed a sum of $3250 at 8% simple interest for 3 years.
(2) Calculate the amount due if Jessica borrowed a sum of $3750 at 4% simple interest for 3 years.
(3) Calculate the amount due if Patricia borrowed a sum of $3150 at 5% simple interest for 4 years.
(4) If Sandra paid $5162 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(5) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $8424 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Sarah borrowed a sum of $5850 at 4% simple interest for 8 years.
(7) In how much time a principal of $3150 will amount to $3339 at a simple interest of 2% per annum?
(8) 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.
(9) Find the amount to be paid if Linda borrowed a sum of $5350 at 3% simple interest for 8 years.
(10) Find the amount to be paid if Michael borrowed a sum of $5300 at 5% simple interest for 7 years.