Question:
How much loan did Carol borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7755 to clear it?
Correct Answer
$7050
Solution And Explanation
Solution
Given,
Amount (A) = $7755
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
$7755 = P (1 + 2% × 5)
⇒ $7755 = P (1 + 2/100 × 5)
⇒ $7755 = P (1 + 2 × 5/100)
⇒ $7755 = P (1 + 10/100)
⇒ $7755 = P (100 + 10/100)
⇒ $7755 = P × 110/100
⇒ P × 110/100 = $7755
⇒ P = 7755/110/100
⇒ P = 7755 × 100/110
⇒ P = 7755 × 100/110
⇒ P = 775500/110
⇒ P = $7050
Thus, the sum borrowed (P) = $7050 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 7755, then the Principal = 100/110 × 7755
= 100 × 7755/110
= 775500/110
= 7050
Thus, Principal = $7050
Thus, the sum borrowed = $7050 Answer
Similar Questions
(1) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 8% simple interest?
(2) Calculate the amount due if Christopher borrowed a sum of $4000 at 10% simple interest for 3 years.
(3) How much loan did Joseph borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6840 to clear it?
(4) Find the amount to be paid if Patricia borrowed a sum of $5150 at 8% simple interest for 7 years.
(5) Calculate the amount due if William borrowed a sum of $3500 at 7% simple interest for 3 years.
(6) Calculate the amount due if William borrowed a sum of $3500 at 4% simple interest for 4 years.
(7) If Nancy paid $4980 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(8) In how much time a principal of $3050 will amount to $3660 at a simple interest of 5% per annum?
(9) If Ashley paid $5096 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(10) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $10010 to clear the loan, then find the time period of the loan.