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) How much loan did Kevin borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8875 to clear it?
(2) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $10920 to clear the loan, then find the time period of the loan.
(3) Susan had to pay $4197.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(4) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 10% simple interest?
(5) Find the amount to be paid if Barbara borrowed a sum of $5550 at 10% simple interest for 8 years.
(6) Calculate the amount due if Patricia borrowed a sum of $3150 at 3% simple interest for 3 years.
(7) What amount will be due after 2 years if David borrowed a sum of $3200 at a 8% simple interest?
(8) How much loan did Christopher borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6900 to clear it?
(9) Find the amount to be paid if Michael borrowed a sum of $5300 at 9% simple interest for 7 years.
(10) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $11590 to clear the loan, then find the time period of the loan.