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) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $7396 to clear the loan, then find the time period of the loan.
(2) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $12920 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Joseph borrowed a sum of $3700 at 10% simple interest for 3 years.
(4) How much loan did Carol borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8460 to clear it?
(5) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $11584 to clear the loan, then find the time period of the loan.
(6) How much loan did Jacob borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $10000 to clear it?
(7) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $10370 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 6% simple interest.
(9) Calculate the amount due if John borrowed a sum of $3200 at 10% simple interest for 4 years.
(10) How much loan did Sandra borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7740 to clear it?