Question:
If Barbara paid $3834 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
Correct Answer
$3550
Solution And Explanation
Solution
Given,
Amount (A) = $3834
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
$3834 = P (1 + 2% × 4)
⇒ $3834 = P (1 + 2/100 × 4)
⇒ $3834 = P (1 + 2 × 4/100)
⇒ $3834 = P (1 + 8/100)
⇒ $3834 = P (100 + 8/100)
⇒ $3834 = P × 108/100
⇒ P × 108/100 = $3834
⇒ P = 3834/108/100
⇒ P = 3834 × 100/108
⇒ P = 3834 × 100/108
⇒ P = 383400/108
⇒ P = $3550
Thus, the sum borrowed (P) = $3550 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 3834, then the Principal = 100/108 × 3834
= 100 × 3834/108
= 383400/108
= 3550
Thus, Principal = $3550
Thus, the sum borrowed = $3550 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 9% simple interest.
(2) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 9% simple interest.
(3) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $8140 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 8% simple interest.
(5) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 9% simple interest.
(6) If Karen paid $4424 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(7) If Daniel paid $4756 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(8) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 8% simple interest.
(9) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $10030 to clear the loan, then find the time period of the loan.
(10) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $11480 to clear the loan, then find the time period of the loan.