Question:
How much loan did George borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8395 to clear it?
Correct Answer
$7300
Solution And Explanation
Solution
Given,
Amount (A) = $8395
Rate of Simple Interest (R) = 3%
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
$8395 = P (1 + 3% × 5)
⇒ $8395 = P (1 + 3/100 × 5)
⇒ $8395 = P (1 + 3 × 5/100)
⇒ $8395 = P (1 + 15/100)
⇒ $8395 = P (100 + 15/100)
⇒ $8395 = P × 115/100
⇒ P × 115/100 = $8395
⇒ P = 8395/115/100
⇒ P = 8395 × 100/115
⇒ P = 8395 × 100/115
⇒ P = 839500/115
⇒ 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 = 3% per annum
Thus, Interest = 3% of principal
⇒ Interest = 3% of 100 = 3
Thus, Simple Interest for 1 year = 3
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 × 3 = 15
Thus, simple interest for 5 years = 15
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 15 = 115
Calculation of the Principal
Now,
∵ If the Amount is 115, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/115
∴ If the Amount is 8395, then the Principal = 100/115 × 8395
= 100 × 8395/115
= 839500/115
= 7300
Thus, Principal = $7300
Thus, the sum borrowed = $7300 Answer
Similar Questions
(1) If Donald paid $5040 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(2) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $8084 to clear the loan, then find the time period of the loan.
(3) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $9593 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 2% simple interest.
(5) Find the amount to be paid if Robert borrowed a sum of $5100 at 2% simple interest for 7 years.
(6) If Daniel paid $4920 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(7) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 8% simple interest?
(8) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 8% simple interest.
(9) In how much time a principal of $3000 will amount to $3240 at a simple interest of 2% per annum?
(10) Find the amount to be paid if Joseph borrowed a sum of $5700 at 4% simple interest for 8 years.