Question:
How much loan did Brian borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8640 to clear it?
Correct Answer
$7200
Solution And Explanation
Solution
Given,
Amount (A) = $8640
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
$8640 = P (1 + 4% × 5)
⇒ $8640 = P (1 + 4/100 × 5)
⇒ $8640 = P (1 + 4 × 5/100)
⇒ $8640 = P (1 + 20/100)
⇒ $8640 = P (100 + 20/100)
⇒ $8640 = P × 120/100
⇒ P × 120/100 = $8640
⇒ P = 8640/120/100
⇒ P = 8640 × 100/120
⇒ P = 8640 × 100/120
⇒ P = 864000/120
⇒ 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 = 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 8640, then the Principal = 100/120 × 8640
= 100 × 8640/120
= 864000/120
= 7200
Thus, Principal = $7200
Thus, the sum borrowed = $7200 Answer
Similar Questions
(1) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $9828 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 2% simple interest for 8 years.
(3) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 5% simple interest?
(4) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $8740 to clear the loan, then find the time period of the loan.
(5) What amount will be due after 2 years if James borrowed a sum of $3000 at a 5% simple interest?
(6) 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?
(7) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 2% simple interest?
(8) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 10% simple interest?
(9) Find the amount to be paid if Linda borrowed a sum of $5350 at 5% simple interest for 8 years.
(10) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 8% simple interest?