Question:
Emily had to pay $5177.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
Correct Answer
$4750
Solution And Explanation
Solution
Given,
Amount (A) = $5177.5
Rate of Simple Interest (R) = 3%
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
$5177.5 = P (1 + 3% × 3)
⇒ $5177.5 = P (1 + 3/100 × 3)
⇒ $5177.5 = P (1 + 3 × 3/100)
⇒ $5177.5 = P (1 + 9/100)
⇒ $5177.5 = P (100 + 9/100)
⇒ $5177.5 = P × 109/100
⇒ P × 109/100 = $5177.5
⇒ P = 5177.5/109/100
⇒ P = 5177.5 × 100/109
⇒ P = 5177.5 × 100/109
⇒ P = 517750/109
⇒ P = $4750
Thus, the sum borrowed (P) = $4750 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 = 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 × 3 = 9
Thus, simple interest for 3 years = 9
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 9 = 109
Calculation of the Principal
Now,
∵ If the Amount is 109, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/109
∴ If the Amount is 5177.5, then the Principal = 100/109 × 5177.5
= 100 × 5177.5/109
= 517750/109
= 4750
Thus, Principal = $4750
Thus, the sum borrowed = $4750 Answer
Similar Questions
(1) Find the amount to be paid if Michael borrowed a sum of $5300 at 9% simple interest for 7 years.
(2) In how much time a principal of $3150 will amount to $3339 at a simple interest of 2% per annum?
(3) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $7520 to clear the loan, then find the time period of the loan.
(4) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $8436 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if John borrowed a sum of $3200 at 4% simple interest for 3 years.
(6) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 3% simple interest.
(7) Calculate the amount due if James borrowed a sum of $3000 at 4% simple interest for 4 years.
(8) Find the amount to be paid if Joseph borrowed a sum of $5700 at 3% simple interest for 7 years.
(9) Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $8162 to clear the loan, then find the time period of the loan.
(10) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $10800 to clear the loan, then find the time period of the loan.