Question:
How much loan did Nancy borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7072.5 to clear it?
Correct Answer
$6150
Solution And Explanation
Solution
Given,
Amount (A) = $7072.5
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
$7072.5 = P (1 + 3% × 5)
⇒ $7072.5 = P (1 + 3/100 × 5)
⇒ $7072.5 = P (1 + 3 × 5/100)
⇒ $7072.5 = P (1 + 15/100)
⇒ $7072.5 = P (100 + 15/100)
⇒ $7072.5 = P × 115/100
⇒ P × 115/100 = $7072.5
⇒ P = 7072.5/115/100
⇒ P = 7072.5 × 100/115
⇒ P = 7072.5 × 100/115
⇒ P = 707250/115
⇒ P = $6150
Thus, the sum borrowed (P) = $6150 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 7072.5, then the Principal = 100/115 × 7072.5
= 100 × 7072.5/115
= 707250/115
= 6150
Thus, Principal = $6150
Thus, the sum borrowed = $6150 Answer
Similar Questions
(1) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $11390 to clear the loan, then find the time period of the loan.
(2) If Paul paid $5452 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(3) If Matthew paid $4872 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(4) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 4% simple interest.
(5) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $10148 to clear the loan, then find the time period of the loan.
(6) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $9412 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 8% simple interest.
(8) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $10240 to clear the loan, then find the time period of the loan.
(9) Jennifer took a loan of $4500 at the rate of 10% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if Barbara borrowed a sum of $5550 at 3% simple interest for 8 years.