Question:
If Karen paid $4582 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
Correct Answer
$3950
Solution And Explanation
Solution
Given,
Amount (A) = $4582
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
$4582 = P (1 + 4% × 4)
⇒ $4582 = P (1 + 4/100 × 4)
⇒ $4582 = P (1 + 4 × 4/100)
⇒ $4582 = P (1 + 16/100)
⇒ $4582 = P (100 + 16/100)
⇒ $4582 = P × 116/100
⇒ P × 116/100 = $4582
⇒ P = 4582/116/100
⇒ P = 4582 × 100/116
⇒ P = 4582 × 100/116
⇒ P = 458200/116
⇒ P = $3950
Thus, the sum borrowed (P) = $3950 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 4582, then the Principal = 100/116 × 4582
= 100 × 4582/116
= 458200/116
= 3950
Thus, Principal = $3950
Thus, the sum borrowed = $3950 Answer
Similar Questions
(1) How much loan did Christopher borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7200 to clear it?
(2) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 4% simple interest.
(3) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $6556 to clear the loan, then find the time period of the loan.
(4) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $6248 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Mary borrowed a sum of $5050 at 5% simple interest for 7 years.
(6) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $10710 to clear the loan, then find the time period of the loan.
(7) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.
(8) Nancy had to pay $4648 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(9) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $11400 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 7% simple interest for 7 years.