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) How much loan did Christopher borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6600 to clear it?
(2) How much loan did Stephanie borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9060 to clear it?
(3) Find the amount to be paid if Mary borrowed a sum of $5050 at 5% simple interest for 7 years.
(4) If Matthew paid $4536 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(5) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $10492 to clear the loan, then find the time period of the loan.
(6) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 7% simple interest?
(7) Find the amount to be paid if Robert borrowed a sum of $5100 at 4% simple interest for 8 years.
(8) Calculate the amount due if Linda borrowed a sum of $3350 at 9% simple interest for 3 years.
(9) 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.
(10) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $7335 to clear the loan, then find the time period of the loan.