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) Find the amount to be paid if William borrowed a sum of $5500 at 5% simple interest for 8 years.
(2) How much loan did Kevin borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8520 to clear it?
(3) Find the amount to be paid if Linda borrowed a sum of $5350 at 9% simple interest for 7 years.
(4) 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.
(5) Calculate the amount due if Thomas borrowed a sum of $3800 at 2% simple interest for 3 years.
(6) Calculate the amount due if Linda borrowed a sum of $3350 at 3% simple interest for 4 years.
(7) 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.
(8) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 2% simple interest.
(9) Find the amount to be paid if Barbara borrowed a sum of $5550 at 10% simple interest for 8 years.
(10) Find the amount to be paid if John borrowed a sum of $5200 at 9% simple interest for 7 years.