Question:
How much loan did Robert borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5610 to clear it?
Correct Answer
$5100
Solution And Explanation
Solution
Given,
Amount (A) = $5610
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
$5610 = P (1 + 2% × 5)
⇒ $5610 = P (1 + 2/100 × 5)
⇒ $5610 = P (1 + 2 × 5/100)
⇒ $5610 = P (1 + 10/100)
⇒ $5610 = P (100 + 10/100)
⇒ $5610 = P × 110/100
⇒ P × 110/100 = $5610
⇒ P = 5610/110/100
⇒ P = 5610 × 100/110
⇒ P = 5610 × 100/110
⇒ P = 561000/110
⇒ P = $5100
Thus, the sum borrowed (P) = $5100 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 5610, then the Principal = 100/110 × 5610
= 100 × 5610/110
= 561000/110
= 5100
Thus, Principal = $5100
Thus, the sum borrowed = $5100 Answer
Similar Questions
(1) Calculate the amount due if Michael borrowed a sum of $3300 at 6% simple interest for 4 years.
(2) Find the amount to be paid if Robert borrowed a sum of $5100 at 7% simple interest for 8 years.
(3) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 5% simple interest.
(4) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 6% simple interest?
(5) In how much time a principal of $3050 will amount to $3507.5 at a simple interest of 3% per annum?
(6) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $9720 to clear the loan, then find the time period of the loan.
(7) If Barbara paid $3976 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(8) If Christopher borrowed $4000 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(9) Calculate the amount due if James borrowed a sum of $3000 at 8% simple interest for 3 years.
(10) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 5% simple interest.