Question:
If Anthony paid $4988 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
Correct Answer
$4300
Solution And Explanation
Solution
Given,
Amount (A) = $4988
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
$4988 = P (1 + 4% × 4)
⇒ $4988 = P (1 + 4/100 × 4)
⇒ $4988 = P (1 + 4 × 4/100)
⇒ $4988 = P (1 + 16/100)
⇒ $4988 = P (100 + 16/100)
⇒ $4988 = P × 116/100
⇒ P × 116/100 = $4988
⇒ P = 4988/116/100
⇒ P = 4988 × 100/116
⇒ P = 4988 × 100/116
⇒ P = 498800/116
⇒ P = $4300
Thus, the sum borrowed (P) = $4300 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 4988, then the Principal = 100/116 × 4988
= 100 × 4988/116
= 498800/116
= 4300
Thus, Principal = $4300
Thus, the sum borrowed = $4300 Answer
Similar Questions
(1) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 10% simple interest?
(2) Calculate the amount due if Michael borrowed a sum of $3300 at 3% simple interest for 4 years.
(3) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 10% simple interest.
(4) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 6% simple interest.
(5) Calculate the amount due if Sarah borrowed a sum of $3850 at 7% simple interest for 3 years.
(6) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $11210 to clear the loan, then find the time period of the loan.
(7) How much loan did William borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6050 to clear it?
(8) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 2% simple interest.
(9) Find the amount to be paid if Christopher borrowed a sum of $6000 at 9% simple interest for 8 years.
(10) Calculate the amount due if Sarah borrowed a sum of $3850 at 10% simple interest for 3 years.