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) Calculate the amount due if Charles borrowed a sum of $3900 at 8% simple interest for 3 years.
(2) Find the amount to be paid if Christopher borrowed a sum of $6000 at 6% simple interest for 8 years.
(3) If Christopher paid $4320 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(4) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 7% simple interest.
(5) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $7332 to clear the loan, then find the time period of the loan.
(6) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $10836 to clear the loan, then find the time period of the loan.
(7) If Steven paid $5520 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(8) Find the amount to be paid if Michael borrowed a sum of $5300 at 4% simple interest for 7 years.
(9) How much loan did Robert borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5610 to clear it?
(10) Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $9943 to clear the loan, then find the time period of the loan.