Question:
How much loan did Mark borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7680 to clear it?
Correct Answer
$6400
Solution And Explanation
Solution
Given,
Amount (A) = $7680
Rate of Simple Interest (R) = 4%
Time (T) = 5 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
$7680 = P (1 + 4% × 5)
⇒ $7680 = P (1 + 4/100 × 5)
⇒ $7680 = P (1 + 4 × 5/100)
⇒ $7680 = P (1 + 20/100)
⇒ $7680 = P (100 + 20/100)
⇒ $7680 = P × 120/100
⇒ P × 120/100 = $7680
⇒ P = 7680/120/100
⇒ P = 7680 × 100/120
⇒ P = 7680 × 100/120
⇒ P = 768000/120
⇒ P = $6400
Thus, the sum borrowed (P) = $6400 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 = 5 years
So, we need to calculate the simple interest for the given time period, which is 5 years
Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year
= 5 × 4 = 20
Thus, simple interest for 5 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 7680, then the Principal = 100/120 × 7680
= 100 × 7680/120
= 768000/120
= 6400
Thus, Principal = $6400
Thus, the sum borrowed = $6400 Answer
Similar Questions
(1) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $11340 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Christopher borrowed a sum of $6000 at 10% simple interest for 7 years.
(3) Find the amount to be paid if Charles borrowed a sum of $5900 at 9% simple interest for 7 years.
(4) 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.
(5) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 6% simple interest.
(6) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $7820 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 3% simple interest.
(8) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $9617 to clear the loan, then find the time period of the loan.
(9) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $9514 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if Thomas borrowed a sum of $5800 at 7% simple interest for 8 years.