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 after 9 years if Barbara borrowed a sum of $5550 at a rate of 8% simple interest.
(2) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 9% simple interest?
(3) What amount will be due after 2 years if William borrowed a sum of $3250 at a 5% simple interest?
(4) Find the amount to be paid if James borrowed a sum of $5000 at 9% simple interest for 8 years.
(5) Calculate the amount due if Michael borrowed a sum of $3300 at 2% simple interest for 4 years.
(6) Charles had to pay $4485 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(7) How much loan did Anthony borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6930 to clear it?
(8) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $7700 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Joseph borrowed a sum of $3700 at 4% simple interest for 4 years.
(10) Daniel had to pay $4592 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.