Question:
How much loan did Matthew borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6820 to clear it?
Correct Answer
$6200
Solution And Explanation
Solution
Given,
Amount (A) = $6820
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
$6820 = P (1 + 2% × 5)
⇒ $6820 = P (1 + 2/100 × 5)
⇒ $6820 = P (1 + 2 × 5/100)
⇒ $6820 = P (1 + 10/100)
⇒ $6820 = P (100 + 10/100)
⇒ $6820 = P × 110/100
⇒ P × 110/100 = $6820
⇒ P = 6820/110/100
⇒ P = 6820 × 100/110
⇒ P = 6820 × 100/110
⇒ P = 682000/110
⇒ P = $6200
Thus, the sum borrowed (P) = $6200 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 6820, then the Principal = 100/110 × 6820
= 100 × 6820/110
= 682000/110
= 6200
Thus, Principal = $6200
Thus, the sum borrowed = $6200 Answer
Similar Questions
(1) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 6% simple interest?
(2) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $10030 to clear the loan, then find the time period of the loan.
(3) What amount will be due after 2 years if David borrowed a sum of $3200 at a 9% simple interest?
(4) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $12540 to clear the loan, then find the time period of the loan.
(5) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 2% simple interest?
(6) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $7360 to clear the loan, then find the time period of the loan.
(7) Richard had to pay $4032 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(8) Calculate the amount due if Sarah borrowed a sum of $3850 at 2% simple interest for 3 years.
(9) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 4% simple interest.
(10) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 6% simple interest.