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 Joseph borrowed a sum of $5700 at 10% simple interest for 8 years.
(2) Find the amount to be paid if Patricia borrowed a sum of $5150 at 7% simple interest for 8 years.
(3) Find the amount to be paid if Karen borrowed a sum of $5950 at 2% simple interest for 8 years.
(4) Calculate the amount due if Richard borrowed a sum of $3600 at 4% simple interest for 4 years.
(5) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 5% simple interest for 7 years.
(6) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $11400 to clear the loan, then find the time period of the loan.
(7) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $8364 to clear the loan, then find the time period of the loan.
(8) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 10% simple interest?
(9) What amount does John have to pay after 6 years if he takes a loan of $3200 at 5% simple interest?
(10) Find the amount to be paid if Barbara borrowed a sum of $5550 at 7% simple interest for 8 years.