Question:
How much loan did Jacob borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8800 to clear it?
Correct Answer
$8000
Solution And Explanation
Solution
Given,
Amount (A) = $8800
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
$8800 = P (1 + 2% × 5)
⇒ $8800 = P (1 + 2/100 × 5)
⇒ $8800 = P (1 + 2 × 5/100)
⇒ $8800 = P (1 + 10/100)
⇒ $8800 = P (100 + 10/100)
⇒ $8800 = P × 110/100
⇒ P × 110/100 = $8800
⇒ P = 8800/110/100
⇒ P = 8800 × 100/110
⇒ P = 8800 × 100/110
⇒ P = 880000/110
⇒ P = $8000
Thus, the sum borrowed (P) = $8000 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 8800, then the Principal = 100/110 × 8800
= 100 × 8800/110
= 880000/110
= 8000
Thus, Principal = $8000
Thus, the sum borrowed = $8000 Answer
Similar Questions
(1) How much loan did Sharon borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9687.5 to clear it?
(2) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 9% simple interest.
(3) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $7560 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 4% simple interest for 8 years.
(5) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 9% simple interest.
(6) How much loan did Linda borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6687.5 to clear it?
(7) In how much time a principal of $3000 will amount to $3270 at a simple interest of 3% per annum?
(8) What amount will be due after 2 years if John borrowed a sum of $3100 at a 9% simple interest?
(9) Find the amount to be paid if John borrowed a sum of $5200 at 5% simple interest for 8 years.
(10) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 10% simple interest.