Question:
How much loan did Karen borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6842.5 to clear it?
Correct Answer
$5950
Solution And Explanation
Solution
Given,
Amount (A) = $6842.5
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
$6842.5 = P (1 + 3% × 5)
⇒ $6842.5 = P (1 + 3/100 × 5)
⇒ $6842.5 = P (1 + 3 × 5/100)
⇒ $6842.5 = P (1 + 15/100)
⇒ $6842.5 = P (100 + 15/100)
⇒ $6842.5 = P × 115/100
⇒ P × 115/100 = $6842.5
⇒ P = 6842.5/115/100
⇒ P = 6842.5 × 100/115
⇒ P = 6842.5 × 100/115
⇒ P = 684250/115
⇒ 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 = 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 6842.5, then the Principal = 100/115 × 6842.5
= 100 × 6842.5/115
= 684250/115
= 5950
Thus, Principal = $5950
Thus, the sum borrowed = $5950 Answer
Similar Questions
(1) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $8946 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Jessica borrowed a sum of $5750 at 9% simple interest for 8 years.
(3) How much loan did Brian borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8280 to clear it?
(4) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.
(5) Kenneth had to pay $5300 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(6) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 5% simple interest?
(7) If Donna paid $5820 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(8) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 6% simple interest.
(9) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 7% simple interest?
(10) How much loan did Brian borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9000 to clear it?