Question:
How much loan did Kevin borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7810 to clear it?
Correct Answer
$7100
Solution And Explanation
Solution
Given,
Amount (A) = $7810
Rate of Simple Interest (R) = 2%
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
$7810 = P (1 + 2% × 5)
⇒ $7810 = P (1 + 2/100 × 5)
⇒ $7810 = P (1 + 2 × 5/100)
⇒ $7810 = P (1 + 10/100)
⇒ $7810 = P (100 + 10/100)
⇒ $7810 = P × 110/100
⇒ P × 110/100 = $7810
⇒ P = 7810/110/100
⇒ P = 7810 × 100/110
⇒ P = 7810 × 100/110
⇒ P = 781000/110
⇒ P = $7100
Thus, the sum borrowed (P) = $7100 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 = 2% per annum
Thus, Interest = 2% of principal
⇒ Interest = 2% of 100 = 2
Thus, Simple Interest for 1 year = 2
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 × 2 = 10
Thus, simple interest for 5 years = 10
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 10 = 110
Calculation of the Principal
Now,
∵ If the Amount is 110, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/110
∴ If the Amount is 7810, then the Principal = 100/110 × 7810
= 100 × 7810/110
= 781000/110
= 7100
Thus, Principal = $7100
Thus, the sum borrowed = $7100 Answer
Similar Questions
(1) If Kenneth paid $5400 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(2) Calculate the amount due if Barbara borrowed a sum of $3550 at 10% simple interest for 4 years.
(3) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $9088 to clear the loan, then find the time period of the loan.
(4) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $9086 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Barbara borrowed a sum of $3550 at 6% simple interest for 3 years.
(6) Calculate the amount due if David borrowed a sum of $3400 at 7% simple interest for 4 years.
(7) Calculate the amount due if Joseph borrowed a sum of $3700 at 4% simple interest for 4 years.
(8) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $8000 to clear the loan, then find the time period of the loan.
(9) William had to pay $4025 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(10) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $8313 to clear the loan, then find the time period of the loan.