Question:
How much loan did Edward borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9500 to clear it?
Correct Answer
$7600
Solution And Explanation
Solution
Given,
Amount (A) = $9500
Rate of Simple Interest (R) = 5%
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
$9500 = P (1 + 5% × 5)
⇒ $9500 = P (1 + 5/100 × 5)
⇒ $9500 = P (1 + 5 × 5/100)
⇒ $9500 = P (1 + 25/100)
⇒ $9500 = P (100 + 25/100)
⇒ $9500 = P × 125/100
⇒ P × 125/100 = $9500
⇒ P = 9500/125/100
⇒ P = 9500 × 100/125
⇒ P = 9500 × 100/125
⇒ P = 950000/125
⇒ P = $7600
Thus, the sum borrowed (P) = $7600 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 = 5% per annum
Thus, Interest = 5% of principal
⇒ Interest = 5% of 100 = 5
Thus, Simple Interest for 1 year = 5
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 × 5 = 25
Thus, simple interest for 5 years = 25
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 25 = 125
Calculation of the Principal
Now,
∵ If the Amount is 125, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/125
∴ If the Amount is 9500, then the Principal = 100/125 × 9500
= 100 × 9500/125
= 950000/125
= 7600
Thus, Principal = $7600
Thus, the sum borrowed = $7600 Answer
Similar Questions
(1) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $7009 to clear the loan, then find the time period of the loan.
(2) How much loan did Michelle borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7992.5 to clear it?
(3) Find the amount to be paid if Sarah borrowed a sum of $5850 at 7% simple interest for 7 years.
(4) Find the amount to be paid if Susan borrowed a sum of $5650 at 9% simple interest for 8 years.
(5) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 7% simple interest.
(6) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $8670 to clear the loan, then find the time period of the loan.
(7) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $11400 to clear the loan, then find the time period of the loan.
(8) In how much time a principal of $3150 will amount to $3622.5 at a simple interest of 5% per annum?
(9) Calculate the amount due if Christopher borrowed a sum of $4000 at 4% simple interest for 3 years.
(10) In how much time a principal of $3000 will amount to $3180 at a simple interest of 2% per annum?