Question:
How much loan did Lisa borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6957.5 to clear it?
Correct Answer
$6050
Solution And Explanation
Solution
Given,
Amount (A) = $6957.5
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
$6957.5 = P (1 + 3% × 5)
⇒ $6957.5 = P (1 + 3/100 × 5)
⇒ $6957.5 = P (1 + 3 × 5/100)
⇒ $6957.5 = P (1 + 15/100)
⇒ $6957.5 = P (100 + 15/100)
⇒ $6957.5 = P × 115/100
⇒ P × 115/100 = $6957.5
⇒ P = 6957.5/115/100
⇒ P = 6957.5 × 100/115
⇒ P = 6957.5 × 100/115
⇒ P = 695750/115
⇒ P = $6050
Thus, the sum borrowed (P) = $6050 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 6957.5, then the Principal = 100/115 × 6957.5
= 100 × 6957.5/115
= 695750/115
= 6050
Thus, Principal = $6050
Thus, the sum borrowed = $6050 Answer
Similar Questions
(1) Calculate the amount due if Robert borrowed a sum of $3100 at 9% simple interest for 4 years.
(2) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $8507 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Richard borrowed a sum of $5600 at 5% simple interest for 7 years.
(4) John had to pay $3680 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(5) Calculate the amount due if Karen borrowed a sum of $3950 at 5% simple interest for 4 years.
(6) Calculate the amount due if James borrowed a sum of $3000 at 9% simple interest for 4 years.
(7) How much loan did Stephanie borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8682.5 to clear it?
(8) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $12160 to clear the loan, then find the time period of the loan.
(9) How much loan did Anthony borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6930 to clear it?
(10) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6562.5 to clear it?