Question:
How much loan did John borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6240 to clear it?
Correct Answer
$5200
Solution And Explanation
Solution
Given,
Amount (A) = $6240
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
$6240 = P (1 + 4% × 5)
⇒ $6240 = P (1 + 4/100 × 5)
⇒ $6240 = P (1 + 4 × 5/100)
⇒ $6240 = P (1 + 20/100)
⇒ $6240 = P (100 + 20/100)
⇒ $6240 = P × 120/100
⇒ P × 120/100 = $6240
⇒ P = 6240/120/100
⇒ P = 6240 × 100/120
⇒ P = 6240 × 100/120
⇒ P = 624000/120
⇒ P = $5200
Thus, the sum borrowed (P) = $5200 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 6240, then the Principal = 100/120 × 6240
= 100 × 6240/120
= 624000/120
= 5200
Thus, Principal = $5200
Thus, the sum borrowed = $5200 Answer
Similar Questions
(1) Calculate the amount due if Joseph borrowed a sum of $3700 at 4% simple interest for 4 years.
(2) How much loan did Robert borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6375 to clear it?
(3) How much loan did Mary borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6060 to clear it?
(4) If Barbara paid $3976 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(5) Calculate the amount due if Richard borrowed a sum of $3600 at 9% simple interest for 4 years.
(6) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 3% simple interest.
(7) Find the amount to be paid if Barbara borrowed a sum of $5550 at 10% simple interest for 7 years.
(8) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 7% simple interest for 8 years.
(9) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 8% simple interest.
(10) Calculate the amount due if Charles borrowed a sum of $3900 at 5% simple interest for 3 years.