Question:
How much loan did Stephanie borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9060 to clear it?
Correct Answer
$7550
Solution And Explanation
Solution
Given,
Amount (A) = $9060
Rate of Simple Interest (R) = 4%
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
$9060 = P (1 + 4% × 5)
⇒ $9060 = P (1 + 4/100 × 5)
⇒ $9060 = P (1 + 4 × 5/100)
⇒ $9060 = P (1 + 20/100)
⇒ $9060 = P (100 + 20/100)
⇒ $9060 = P × 120/100
⇒ P × 120/100 = $9060
⇒ P = 9060/120/100
⇒ P = 9060 × 100/120
⇒ P = 9060 × 100/120
⇒ P = 906000/120
⇒ P = $7550
Thus, the sum borrowed (P) = $7550 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 = 4% per annum
Thus, Interest = 4% of principal
⇒ Interest = 4% of 100 = 4
Thus, Simple Interest for 1 year = 4
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 × 4 = 20
Thus, simple interest for 5 years = 20
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 20 = 120
Calculation of the Principal
Now,
∵ If the Amount is 120, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/120
∴ If the Amount is 9060, then the Principal = 100/120 × 9060
= 100 × 9060/120
= 906000/120
= 7550
Thus, Principal = $7550
Thus, the sum borrowed = $7550 Answer
Similar Questions
(1) How much loan did David borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6750 to clear it?
(2) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 9% simple interest?
(3) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $9600 to clear the loan, then find the time period of the loan.
(4) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 4% simple interest?
(5) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $11352 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Linda borrowed a sum of $5350 at 2% simple interest for 7 years.
(7) How much loan did Michelle borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8687.5 to clear it?
(8) In how much time a principal of $3050 will amount to $3538 at a simple interest of 4% per annum?
(9) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 8% simple interest.
(10) Find the amount to be paid if John borrowed a sum of $5200 at 2% simple interest for 7 years.