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) Calculate the amount due if Joseph borrowed a sum of $3700 at 8% simple interest for 4 years.
(2) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 8% simple interest?
(3) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 6% simple interest?
(4) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 7% simple interest?
(5) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 7% simple interest.
(6) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $13300 to clear the loan, then find the time period of the loan.
(7) What amount will be due after 2 years if David borrowed a sum of $3200 at a 8% simple interest?
(8) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 5% simple interest.
(9) How much loan did Richard borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6160 to clear it?
(10) What amount will be due after 2 years if James borrowed a sum of $3000 at a 10% simple interest?