Question:
If Sarah paid $4158 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
Correct Answer
$3850
Solution And Explanation
Solution
Given,
Amount (A) = $4158
Rate of Simple Interest (R) = 2%
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
$4158 = P (1 + 2% × 4)
⇒ $4158 = P (1 + 2/100 × 4)
⇒ $4158 = P (1 + 2 × 4/100)
⇒ $4158 = P (1 + 8/100)
⇒ $4158 = P (100 + 8/100)
⇒ $4158 = P × 108/100
⇒ P × 108/100 = $4158
⇒ P = 4158/108/100
⇒ P = 4158 × 100/108
⇒ P = 4158 × 100/108
⇒ P = 415800/108
⇒ P = $3850
Thus, the sum borrowed (P) = $3850 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 = 2% per annum
Thus, Interest = 2% of principal
⇒ Interest = 2% of 100 = 2
Thus, Simple Interest for 1 year = 2
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 × 2 = 8
Thus, simple interest for 4 years = 8
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 8 = 108
Calculation of the Principal
Now,
∵ If the Amount is 108, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/108
∴ If the Amount is 4158, then the Principal = 100/108 × 4158
= 100 × 4158/108
= 415800/108
= 3850
Thus, Principal = $3850
Thus, the sum borrowed = $3850 Answer
Similar Questions
(1) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $9440 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 2% simple interest for 8 years.
(3) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 2% simple interest.
(4) Calculate the amount due if Patricia borrowed a sum of $3150 at 3% simple interest for 4 years.
(5) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $10860 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Joseph borrowed a sum of $5700 at 10% simple interest for 8 years.
(7) How much loan did Joseph borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6270 to clear it?
(8) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $9010 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Sarah borrowed a sum of $3850 at 7% simple interest for 4 years.
(10) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $10030 to clear the loan, then find the time period of the loan.