Question:
How much loan did Timothy borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8510 to clear it?
Correct Answer
$7400
Solution And Explanation
Solution
Given,
Amount (A) = $8510
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
$8510 = P (1 + 3% × 5)
⇒ $8510 = P (1 + 3/100 × 5)
⇒ $8510 = P (1 + 3 × 5/100)
⇒ $8510 = P (1 + 15/100)
⇒ $8510 = P (100 + 15/100)
⇒ $8510 = P × 115/100
⇒ P × 115/100 = $8510
⇒ P = 8510/115/100
⇒ P = 8510 × 100/115
⇒ P = 8510 × 100/115
⇒ P = 851000/115
⇒ P = $7400
Thus, the sum borrowed (P) = $7400 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 8510, then the Principal = 100/115 × 8510
= 100 × 8510/115
= 851000/115
= 7400
Thus, Principal = $7400
Thus, the sum borrowed = $7400 Answer
Similar Questions
(1) How much loan did Deborah borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9312.5 to clear it?
(2) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $8280 to clear the loan, then find the time period of the loan.
(3) How much loan did Lisa borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7562.5 to clear it?
(4) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 6% simple interest.
(5) Find the amount to be paid if Patricia borrowed a sum of $5150 at 8% simple interest for 8 years.
(6) Find the amount to be paid if Thomas borrowed a sum of $5800 at 3% simple interest for 7 years.
(7) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $11000 to clear the loan, then find the time period of the loan.
(8) How much loan did Lisa borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6655 to clear it?
(9) If Richard paid $3888 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(10) If Richard paid $4032 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.