Question:
How much loan did Karen borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7437.5 to clear it?
Correct Answer
$5950
Solution And Explanation
Solution
Given,
Amount (A) = $7437.5
Rate of Simple Interest (R) = 5%
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
$7437.5 = P (1 + 5% × 5)
⇒ $7437.5 = P (1 + 5/100 × 5)
⇒ $7437.5 = P (1 + 5 × 5/100)
⇒ $7437.5 = P (1 + 25/100)
⇒ $7437.5 = P (100 + 25/100)
⇒ $7437.5 = P × 125/100
⇒ P × 125/100 = $7437.5
⇒ P = 7437.5/125/100
⇒ P = 7437.5 × 100/125
⇒ P = 7437.5 × 100/125
⇒ P = 743750/125
⇒ P = $5950
Thus, the sum borrowed (P) = $5950 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 = 5% per annum
Thus, Interest = 5% of principal
⇒ Interest = 5% of 100 = 5
Thus, Simple Interest for 1 year = 5
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 × 5 = 25
Thus, simple interest for 5 years = 25
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 25 = 125
Calculation of the Principal
Now,
∵ If the Amount is 125, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/125
∴ If the Amount is 7437.5, then the Principal = 100/125 × 7437.5
= 100 × 7437.5/125
= 743750/125
= 5950
Thus, Principal = $5950
Thus, the sum borrowed = $5950 Answer
Similar Questions
(1) If Michelle paid $5544 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(2) If James paid $3600 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(3) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $7020 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 10% simple interest.
(5) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 6% simple interest?
(6) Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $8480 to clear the loan, then find the time period of the loan.
(7) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $9204 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 10% simple interest for 7 years.
(9) Find the amount to be paid if David borrowed a sum of $5400 at 2% simple interest for 7 years.
(10) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $6800 to clear the loan, then find the time period of the loan.