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 Michael borrowed a sum of $3300 at 8% simple interest for 4 years.
(2) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 6% simple interest for 8 years.
(3) How much loan did Laura borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9812.5 to clear it?
(4) What amount will be due after 2 years if John borrowed a sum of $3100 at a 5% simple interest?
(5) Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $10296 to clear the loan, then find the time period of the loan.
(6) How much loan did Edward borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9120 to clear it?
(7) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $7560 to clear the loan, then find the time period of the loan.
(8) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8700 to clear it?
(9) If Elizabeth paid $4140 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(10) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 4% simple interest?