Question:
How much loan did William borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6050 to clear it?
Correct Answer
$5500
Solution And Explanation
Solution
Given,
Amount (A) = $6050
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
$6050 = P (1 + 2% × 5)
⇒ $6050 = P (1 + 2/100 × 5)
⇒ $6050 = P (1 + 2 × 5/100)
⇒ $6050 = P (1 + 10/100)
⇒ $6050 = P (100 + 10/100)
⇒ $6050 = P × 110/100
⇒ P × 110/100 = $6050
⇒ P = 6050/110/100
⇒ P = 6050 × 100/110
⇒ P = 6050 × 100/110
⇒ P = 605000/110
⇒ P = $5500
Thus, the sum borrowed (P) = $5500 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 6050, then the Principal = 100/110 × 6050
= 100 × 6050/110
= 605000/110
= 5500
Thus, Principal = $5500
Thus, the sum borrowed = $5500 Answer
Similar Questions
(1) Find the amount to be paid if Robert borrowed a sum of $5100 at 4% simple interest for 8 years.
(2) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $10080 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Charles borrowed a sum of $3900 at 8% simple interest for 4 years.
(4) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $8732 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 7% simple interest for 7 years.
(6) Find the amount to be paid if David borrowed a sum of $5400 at 7% simple interest for 8 years.
(7) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 5% simple interest?
(8) Find the amount to be paid if Thomas borrowed a sum of $5800 at 3% simple interest for 8 years.
(9) Calculate the amount due if Sarah borrowed a sum of $3850 at 5% simple interest for 3 years.
(10) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $11600 to clear the loan, then find the time period of the loan.