Question:
How much loan did Brian borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8280 to clear it?
Correct Answer
$7200
Solution And Explanation
Solution
Given,
Amount (A) = $8280
Rate of Simple Interest (R) = 3%
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
$8280 = P (1 + 3% × 5)
⇒ $8280 = P (1 + 3/100 × 5)
⇒ $8280 = P (1 + 3 × 5/100)
⇒ $8280 = P (1 + 15/100)
⇒ $8280 = P (100 + 15/100)
⇒ $8280 = P × 115/100
⇒ P × 115/100 = $8280
⇒ P = 8280/115/100
⇒ P = 8280 × 100/115
⇒ P = 8280 × 100/115
⇒ P = 828000/115
⇒ 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 = 3% per annum
Thus, Interest = 3% of principal
⇒ Interest = 3% of 100 = 3
Thus, Simple Interest for 1 year = 3
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 × 3 = 15
Thus, simple interest for 5 years = 15
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 15 = 115
Calculation of the Principal
Now,
∵ If the Amount is 115, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/115
∴ If the Amount is 8280, then the Principal = 100/115 × 8280
= 100 × 8280/115
= 828000/115
= 7200
Thus, Principal = $7200
Thus, the sum borrowed = $7200 Answer
Similar Questions
(1) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 10% simple interest.
(2) Kenneth had to pay $5750 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(3) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 8% simple interest?
(4) Find the amount to be paid if Robert borrowed a sum of $5100 at 4% simple interest for 8 years.
(5) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 4% simple interest?
(6) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 4% simple interest?
(7) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 9% simple interest?
(8) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $9860 to clear the loan, then find the time period of the loan.
(9) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.
(10) How much loan did Matthew borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7440 to clear it?