Question:
If Michelle paid $5742 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
Correct Answer
$4950
Solution And Explanation
Solution
Given,
Amount (A) = $5742
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
$5742 = P (1 + 4% × 4)
⇒ $5742 = P (1 + 4/100 × 4)
⇒ $5742 = P (1 + 4 × 4/100)
⇒ $5742 = P (1 + 16/100)
⇒ $5742 = P (100 + 16/100)
⇒ $5742 = P × 116/100
⇒ P × 116/100 = $5742
⇒ P = 5742/116/100
⇒ P = 5742 × 100/116
⇒ P = 5742 × 100/116
⇒ P = 574200/116
⇒ P = $4950
Thus, the sum borrowed (P) = $4950 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 5742, then the Principal = 100/116 × 5742
= 100 × 5742/116
= 574200/116
= 4950
Thus, Principal = $4950
Thus, the sum borrowed = $4950 Answer
Similar Questions
(1) Find the amount to be paid if Susan borrowed a sum of $5650 at 4% simple interest for 7 years.
(2) Find the amount to be paid if John borrowed a sum of $5200 at 3% simple interest for 8 years.
(3) 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.
(4) Calculate the amount due if David borrowed a sum of $3400 at 7% simple interest for 4 years.
(5) Find the amount to be paid if James borrowed a sum of $5000 at 10% simple interest for 7 years.
(6) How much loan did David borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5940 to clear it?
(7) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $8378 to clear the loan, then find the time period of the loan.
(8) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $9112 to clear the loan, then find the time period of the loan.
(9) Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $10824 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 7% simple interest.