Question:
How much loan did George borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8030 to clear it?
Correct Answer
$7300
Solution And Explanation
Solution
Given,
Amount (A) = $8030
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
$8030 = P (1 + 2% × 5)
⇒ $8030 = P (1 + 2/100 × 5)
⇒ $8030 = P (1 + 2 × 5/100)
⇒ $8030 = P (1 + 10/100)
⇒ $8030 = P (100 + 10/100)
⇒ $8030 = P × 110/100
⇒ P × 110/100 = $8030
⇒ P = 8030/110/100
⇒ P = 8030 × 100/110
⇒ P = 8030 × 100/110
⇒ P = 803000/110
⇒ P = $7300
Thus, the sum borrowed (P) = $7300 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 8030, then the Principal = 100/110 × 8030
= 100 × 8030/110
= 803000/110
= 7300
Thus, Principal = $7300
Thus, the sum borrowed = $7300 Answer
Similar Questions
(1) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $10080 to clear the loan, then find the time period of the loan.
(2) How much loan did Margaret borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6985 to clear it?
(3) Calculate the amount due if Richard borrowed a sum of $3600 at 8% simple interest for 3 years.
(4) Find the amount to be paid if Thomas borrowed a sum of $5800 at 6% simple interest for 7 years.
(5) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $9288 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Christopher borrowed a sum of $6000 at 8% simple interest for 7 years.
(7) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 3% simple interest.
(8) In how much time a principal of $3150 will amount to $3780 at a simple interest of 5% per annum?
(9) How much loan did Jason borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8470 to clear it?
(10) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 5% simple interest.