Question:
How much loan did Brian borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7920 to clear it?
Correct Answer
$7200
Solution And Explanation
Solution
Given,
Amount (A) = $7920
Rate of Simple Interest (R) = 2%
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
$7920 = P (1 + 2% × 5)
⇒ $7920 = P (1 + 2/100 × 5)
⇒ $7920 = P (1 + 2 × 5/100)
⇒ $7920 = P (1 + 10/100)
⇒ $7920 = P (100 + 10/100)
⇒ $7920 = P × 110/100
⇒ P × 110/100 = $7920
⇒ P = 7920/110/100
⇒ P = 7920 × 100/110
⇒ P = 7920 × 100/110
⇒ P = 792000/110
⇒ P = $7200
Thus, the sum borrowed (P) = $7200 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 = 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 × 2 = 10
Thus, simple interest for 5 years = 10
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 10 = 110
Calculation of the Principal
Now,
∵ If the Amount is 110, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/110
∴ If the Amount is 7920, then the Principal = 100/110 × 7920
= 100 × 7920/110
= 792000/110
= 7200
Thus, Principal = $7200
Thus, the sum borrowed = $7200 Answer
Similar Questions
(1) Find the amount to be paid if Barbara borrowed a sum of $5550 at 5% simple interest for 7 years.
(2) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $6068 to clear the loan, then find the time period of the loan.
(3) How much loan did Deborah borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8567.5 to clear it?
(4) Calculate the amount due if Sarah borrowed a sum of $3850 at 2% simple interest for 3 years.
(5) Calculate the amount due if John borrowed a sum of $3200 at 6% simple interest for 3 years.
(6) If Richard paid $4176 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(7) Calculate the amount due if Linda borrowed a sum of $3350 at 5% simple interest for 4 years.
(8) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 9% simple interest?
(9) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 5% simple interest?
(10) If John paid $3584 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.