Question:
How much loan did Brian borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9000 to clear it?
Correct Answer
$7200
Solution And Explanation
Solution
Given,
Amount (A) = $9000
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
$9000 = P (1 + 5% × 5)
⇒ $9000 = P (1 + 5/100 × 5)
⇒ $9000 = P (1 + 5 × 5/100)
⇒ $9000 = P (1 + 25/100)
⇒ $9000 = P (100 + 25/100)
⇒ $9000 = P × 125/100
⇒ P × 125/100 = $9000
⇒ P = 9000/125/100
⇒ P = 9000 × 100/125
⇒ P = 9000 × 100/125
⇒ P = 900000/125
⇒ P = $7200
Thus, the sum borrowed (P) = $7200 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 9000, then the Principal = 100/125 × 9000
= 100 × 9000/125
= 900000/125
= 7200
Thus, Principal = $7200
Thus, the sum borrowed = $7200 Answer
Similar Questions
(1) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 7% simple interest for 8 years.
(2) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 10% simple interest?
(3) What amount will be due after 2 years if William borrowed a sum of $3250 at a 10% simple interest?
(4) Find the amount to be paid if Thomas borrowed a sum of $5800 at 2% simple interest for 7 years.
(5) Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $10106 to clear the loan, then find the time period of the loan.
(6) How much loan did Andrew borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8160 to clear it?
(7) How much loan did Ronald borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9000 to clear it?
(8) How much loan did Joseph borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6840 to clear it?
(9) What amount will be due after 2 years if William borrowed a sum of $3250 at a 8% simple interest?
(10) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $7380 to clear the loan, then find the time period of the loan.