Question:
If John paid $3840 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
Correct Answer
$3200
Solution And Explanation
Solution
Given,
Amount (A) = $3840
Rate of Simple Interest (R) = 5%
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
$3840 = P (1 + 5% × 4)
⇒ $3840 = P (1 + 5/100 × 4)
⇒ $3840 = P (1 + 5 × 4/100)
⇒ $3840 = P (1 + 20/100)
⇒ $3840 = P (100 + 20/100)
⇒ $3840 = P × 120/100
⇒ P × 120/100 = $3840
⇒ P = 3840/120/100
⇒ P = 3840 × 100/120
⇒ P = 3840 × 100/120
⇒ P = 384000/120
⇒ P = $3200
Thus, the sum borrowed (P) = $3200 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 = 5% per annum
Thus, Interest = 5% of principal
⇒ Interest = 5% of 100 = 5
Thus, Simple Interest for 1 year = 5
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 × 5 = 20
Thus, simple interest for 4 years = 20
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 20 = 120
Calculation of the Principal
Now,
∵ If the Amount is 120, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/120
∴ If the Amount is 3840, then the Principal = 100/120 × 3840
= 100 × 3840/120
= 384000/120
= 3200
Thus, Principal = $3200
Thus, the sum borrowed = $3200 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 5% simple interest.
(2) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 10% simple interest?
(3) Calculate the amount due if Patricia borrowed a sum of $3150 at 2% simple interest for 3 years.
(4) Calculate the amount due if Robert borrowed a sum of $3100 at 9% simple interest for 4 years.
(5) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $10260 to clear the loan, then find the time period of the loan.
(6) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $11765 to clear the loan, then find the time period of the loan.
(7) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $8856 to clear the loan, then find the time period of the loan.
(8) Michael had to pay $3795 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(9) If Andrew paid $5568 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(10) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $8024 to clear the loan, then find the time period of the loan.