Question:
How much loan did Mark borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7040 to clear it?
Correct Answer
$6400
Solution And Explanation
Solution
Given,
Amount (A) = $7040
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
$7040 = P (1 + 2% × 5)
⇒ $7040 = P (1 + 2/100 × 5)
⇒ $7040 = P (1 + 2 × 5/100)
⇒ $7040 = P (1 + 10/100)
⇒ $7040 = P (100 + 10/100)
⇒ $7040 = P × 110/100
⇒ P × 110/100 = $7040
⇒ P = 7040/110/100
⇒ P = 7040 × 100/110
⇒ P = 7040 × 100/110
⇒ P = 704000/110
⇒ P = $6400
Thus, the sum borrowed (P) = $6400 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 7040, then the Principal = 100/110 × 7040
= 100 × 7040/110
= 704000/110
= 6400
Thus, Principal = $6400
Thus, the sum borrowed = $6400 Answer
Similar Questions
(1) Calculate the amount due if Jennifer borrowed a sum of $3250 at 7% simple interest for 3 years.
(2) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $6512 to clear the loan, then find the time period of the loan.
(3) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $8436 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 9% simple interest.
(5) In how much time a principal of $3200 will amount to $3840 at a simple interest of 4% per annum?
(6) Calculate the amount due if Jessica borrowed a sum of $3750 at 8% simple interest for 4 years.
(7) Find the amount to be paid if Joseph borrowed a sum of $5700 at 8% simple interest for 7 years.
(8) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 10% simple interest.
(9) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $11696 to clear the loan, then find the time period of the loan.
(10) What amount will be due after 2 years if John borrowed a sum of $3100 at a 7% simple interest?