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) Calculate the amount due if Linda borrowed a sum of $3350 at 9% simple interest for 3 years.
(2) If Joshua paid $5292 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(3) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $11520 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 4% simple interest.
(5) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 2% simple interest.
(6) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $8000 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 $9617 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 7% simple interest.
(9) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 10% simple interest?
(10) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 4% simple interest.