Question:
How much loan did Mary borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5807.5 to clear it?
Correct Answer
$5050
Solution And Explanation
Solution
Given,
Amount (A) = $5807.5
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
$5807.5 = P (1 + 3% × 5)
⇒ $5807.5 = P (1 + 3/100 × 5)
⇒ $5807.5 = P (1 + 3 × 5/100)
⇒ $5807.5 = P (1 + 15/100)
⇒ $5807.5 = P (100 + 15/100)
⇒ $5807.5 = P × 115/100
⇒ P × 115/100 = $5807.5
⇒ P = 5807.5/115/100
⇒ P = 5807.5 × 100/115
⇒ P = 5807.5 × 100/115
⇒ P = 580750/115
⇒ P = $5050
Thus, the sum borrowed (P) = $5050 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 5807.5, then the Principal = 100/115 × 5807.5
= 100 × 5807.5/115
= 580750/115
= 5050
Thus, Principal = $5050
Thus, the sum borrowed = $5050 Answer
Similar Questions
(1) How much loan did Thomas borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7250 to clear it?
(2) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $7661 to clear the loan, then find the time period of the loan.
(3) In how much time a principal of $3050 will amount to $3233 at a simple interest of 2% per annum?
(4) Calculate the amount due if Sarah borrowed a sum of $3850 at 4% simple interest for 3 years.
(5) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 10% simple interest.
(6) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6622 to clear the loan, then find the time period of the loan.
(7) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $8378 to clear the loan, then find the time period of the loan.
(8) What amount does John have to pay after 5 years if he takes a loan of $3200 at 5% simple interest?
(9) Calculate the amount due if David borrowed a sum of $3400 at 6% simple interest for 3 years.
(10) How much loan did James borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5500 to clear it?