Question:
( 1 of 10 ) 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.
(A) 59
(B) 30.5
(C) 61
(D) 60
You selected
$3436.5
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) If Mary borrowed $3050 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(2) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 7% simple interest.
(3) In how much time a principal of $3100 will amount to $3410 at a simple interest of 2% per annum?
(4) Find the amount to be paid if Jessica borrowed a sum of $5750 at 8% simple interest for 7 years.
(5) How much loan did Steven borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7260 to clear it?
(6) Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $10540 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 9% simple interest.
(8) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $5680 to clear the loan, then find the time period of the loan.
(9) How much loan did Donna borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7535 to clear it?
(10) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $7052 to clear the loan, then find the time period of the loan.