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) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 8% simple interest?
(2) If John paid $3456 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(3) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $9600 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 5% simple interest.
(5) In how much time a principal of $3050 will amount to $3812.5 at a simple interest of 5% per annum?
(6) Find the amount to be paid if Jessica borrowed a sum of $5750 at 7% simple interest for 8 years.
(7) Calculate the amount due if Robert borrowed a sum of $3100 at 7% simple interest for 3 years.
(8) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 6% simple interest?
(9) How much loan did Joseph borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6555 to clear it?
(10) Find the amount to be paid if Christopher borrowed a sum of $6000 at 2% simple interest for 7 years.