Question:
How much loan did Rebecca borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8797.5 to clear it?
Correct Answer
$7650
Solution And Explanation
Solution
Given,
Amount (A) = $8797.5
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
$8797.5 = P (1 + 3% × 5)
⇒ $8797.5 = P (1 + 3/100 × 5)
⇒ $8797.5 = P (1 + 3 × 5/100)
⇒ $8797.5 = P (1 + 15/100)
⇒ $8797.5 = P (100 + 15/100)
⇒ $8797.5 = P × 115/100
⇒ P × 115/100 = $8797.5
⇒ P = 8797.5/115/100
⇒ P = 8797.5 × 100/115
⇒ P = 8797.5 × 100/115
⇒ P = 879750/115
⇒ P = $7650
Thus, the sum borrowed (P) = $7650 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 8797.5, then the Principal = 100/115 × 8797.5
= 100 × 8797.5/115
= 879750/115
= 7650
Thus, Principal = $7650
Thus, the sum borrowed = $7650 Answer
Similar Questions
(1) How much loan did Amanda borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7865 to clear it?
(2) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 3% simple interest.
(3) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $8568 to clear the loan, then find the time period of the loan.
(4) If Jessica borrowed $3750 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(5) Mark had to pay $4796 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(6) If Michelle paid $5346 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(7) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 6% simple interest?
(8) If Sandra paid $4806 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(9) How much loan did Brian borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7920 to clear it?
(10) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $9702 to clear the loan, then find the time period of the loan.