Question:
How much loan did Ashley borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7205 to clear it?
Correct Answer
$6550
Solution And Explanation
Solution
Given,
Amount (A) = $7205
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
$7205 = P (1 + 2% × 5)
⇒ $7205 = P (1 + 2/100 × 5)
⇒ $7205 = P (1 + 2 × 5/100)
⇒ $7205 = P (1 + 10/100)
⇒ $7205 = P (100 + 10/100)
⇒ $7205 = P × 110/100
⇒ P × 110/100 = $7205
⇒ P = 7205/110/100
⇒ P = 7205 × 100/110
⇒ P = 7205 × 100/110
⇒ P = 720500/110
⇒ P = $6550
Thus, the sum borrowed (P) = $6550 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 7205, then the Principal = 100/110 × 7205
= 100 × 7205/110
= 720500/110
= 6550
Thus, Principal = $6550
Thus, the sum borrowed = $6550 Answer
Similar Questions
(1) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $7140 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if Karen borrowed a sum of $3950 at 7% simple interest for 4 years.
(3) How much loan did Kenneth borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8750 to clear it?
(4) David had to pay $3706 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(5) How much loan did Steven borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7920 to clear it?
(6) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 5% simple interest for 7 years.
(7) Calculate the amount due if Joseph borrowed a sum of $3700 at 8% simple interest for 4 years.
(8) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $9780 to clear the loan, then find the time period of the loan.
(9) In how much time a principal of $3100 will amount to $3565 at a simple interest of 3% per annum?
(10) How much loan did Ryan borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8690 to clear it?