Question:
If Christopher paid $4640 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
Correct Answer
$4000
Solution And Explanation
Solution
Given,
Amount (A) = $4640
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
$4640 = P (1 + 4% × 4)
⇒ $4640 = P (1 + 4/100 × 4)
⇒ $4640 = P (1 + 4 × 4/100)
⇒ $4640 = P (1 + 16/100)
⇒ $4640 = P (100 + 16/100)
⇒ $4640 = P × 116/100
⇒ P × 116/100 = $4640
⇒ P = 4640/116/100
⇒ P = 4640 × 100/116
⇒ P = 4640 × 100/116
⇒ P = 464000/116
⇒ P = $4000
Thus, the sum borrowed (P) = $4000 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 4640, then the Principal = 100/116 × 4640
= 100 × 4640/116
= 464000/116
= 4000
Thus, Principal = $4000
Thus, the sum borrowed = $4000 Answer
Similar Questions
(1) Find the amount to be paid if Patricia borrowed a sum of $5150 at 5% simple interest for 7 years.
(2) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 2% simple interest?
(3) Patricia had to pay $3528 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(4) How much loan did Edward borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8740 to clear it?
(5) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $8008 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 4% simple interest.
(7) Calculate the amount due if Michael borrowed a sum of $3300 at 7% simple interest for 4 years.
(8) Karen had to pay $4187 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(9) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $8688 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 4% simple interest.