Question:
Anthony had to pay $4558 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
Correct Answer
$4300
Solution And Explanation
Solution
Given,
Amount (A) = $4558
Rate of Simple Interest (R) = 2%
Time (T) = 3 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
$4558 = P (1 + 2% × 3)
⇒ $4558 = P (1 + 2/100 × 3)
⇒ $4558 = P (1 + 2 × 3/100)
⇒ $4558 = P (1 + 6/100)
⇒ $4558 = P (100 + 6/100)
⇒ $4558 = P × 106/100
⇒ P × 106/100 = $4558
⇒ P = 4558/106/100
⇒ P = 4558 × 100/106
⇒ P = 4558 × 100/106
⇒ P = 455800/106
⇒ P = $4300
Thus, the sum borrowed (P) = $4300 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 = 2% per annum
Thus, Interest = 2% of principal
⇒ Interest = 2% of 100 = 2
Thus, Simple Interest for 1 year = 2
Calculation of the Amount
Since, in the question, time = 3 years
So, we need to calculate the simple interest for the given time period, which is 3 years
Thus, Simple Interest for 3 years = 3 × Simple Interest for 1 year
= 3 × 2 = 6
Thus, simple interest for 3 years = 6
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 6 = 106
Calculation of the Principal
Now,
∵ If the Amount is 106, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/106
∴ If the Amount is 4558, then the Principal = 100/106 × 4558
= 100 × 4558/106
= 455800/106
= 4300
Thus, Principal = $4300
Thus, the sum borrowed = $4300 Answer
Similar Questions
(1) Find the amount to be paid if Joseph borrowed a sum of $5700 at 4% simple interest for 8 years.
(2) Find the amount to be paid if William borrowed a sum of $5500 at 5% simple interest for 8 years.
(3) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 3% simple interest.
(4) If Paul paid $5076 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(5) If Andrew paid $5376 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(6) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $8624 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 7% simple interest.
(8) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8700 to clear it?
(9) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $7344 to clear the loan, then find the time period of the loan.
(10) Joseph had to pay $3922 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.