Question:
If Joseph paid $3996 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
Correct Answer
$3700
Solution And Explanation
Solution
Given,
Amount (A) = $3996
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
$3996 = P (1 + 2% × 4)
⇒ $3996 = P (1 + 2/100 × 4)
⇒ $3996 = P (1 + 2 × 4/100)
⇒ $3996 = P (1 + 8/100)
⇒ $3996 = P (100 + 8/100)
⇒ $3996 = P × 108/100
⇒ P × 108/100 = $3996
⇒ P = 3996/108/100
⇒ P = 3996 × 100/108
⇒ P = 3996 × 100/108
⇒ P = 399600/108
⇒ P = $3700
Thus, the sum borrowed (P) = $3700 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 3996, then the Principal = 100/108 × 3996
= 100 × 3996/108
= 399600/108
= 3700
Thus, Principal = $3700
Thus, the sum borrowed = $3700 Answer
Similar Questions
(1) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $9840 to clear the loan, then find the time period of the loan.
(2) How much loan did David borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6750 to clear it?
(3) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $9940 to clear the loan, then find the time period of the loan.
(4) If Betty paid $4590 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(5) Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $8326 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 7% simple interest.
(7) Find the amount to be paid if Susan borrowed a sum of $5650 at 6% simple interest for 7 years.
(8) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 7% simple interest.
(9) 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.
(10) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $7740 to clear the loan, then find the time period of the loan.