Question:
If Thomas paid $4104 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
Correct Answer
$3800
Solution And Explanation
Solution
Given,
Amount (A) = $4104
Rate of Simple Interest (R) = 2%
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
$4104 = P (1 + 2% × 4)
⇒ $4104 = P (1 + 2/100 × 4)
⇒ $4104 = P (1 + 2 × 4/100)
⇒ $4104 = P (1 + 8/100)
⇒ $4104 = P (100 + 8/100)
⇒ $4104 = P × 108/100
⇒ P × 108/100 = $4104
⇒ P = 4104/108/100
⇒ P = 4104 × 100/108
⇒ P = 4104 × 100/108
⇒ P = 410400/108
⇒ P = $3800
Thus, the sum borrowed (P) = $3800 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 = 2% per annum
Thus, Interest = 2% of principal
⇒ Interest = 2% of 100 = 2
Thus, Simple Interest for 1 year = 2
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 × 2 = 8
Thus, simple interest for 4 years = 8
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 8 = 108
Calculation of the Principal
Now,
∵ If the Amount is 108, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/108
∴ If the Amount is 4104, then the Principal = 100/108 × 4104
= 100 × 4104/108
= 410400/108
= 3800
Thus, Principal = $3800
Thus, the sum borrowed = $3800 Answer
Similar Questions
(1) Find the amount to be paid if Michael borrowed a sum of $5300 at 6% simple interest for 7 years.
(2) Find the amount to be paid if Jessica borrowed a sum of $5750 at 6% simple interest for 8 years.
(3) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 6% simple interest?
(4) How much loan did William borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6875 to clear it?
(5) If Mark paid $4752 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(6) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 6% simple interest.
(7) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 5% simple interest?
(8) Calculate the amount due if Patricia borrowed a sum of $3150 at 2% simple interest for 4 years.
(9) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 3% simple interest?
(10) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $6400 to clear the loan, then find the time period of the loan.