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) Find the amount to be paid if Jessica borrowed a sum of $5750 at 10% simple interest for 7 years.
(2) What amount does David have to pay after 6 years if he takes a loan of $3400 at 9% simple interest?
(3) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $7708 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 5% simple interest.
(5) What amount does William have to pay after 5 years if he takes a loan of $3500 at 2% simple interest?
(6) If Emily paid $5320 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(7) Ashley had to pay $4959.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(8) Find the amount to be paid if James borrowed a sum of $5000 at 6% simple interest for 8 years.
(9) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 10% simple interest?
(10) In how much time a principal of $3100 will amount to $3596 at a simple interest of 4% per annum?