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) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $8692 to clear the loan, then find the time period of the loan.
(2) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $7380 to clear the loan, then find the time period of the loan.
(3) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $10212 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if Christopher borrowed a sum of $4000 at 9% simple interest for 3 years.
(5) Calculate the amount due if Sarah borrowed a sum of $3850 at 3% simple interest for 4 years.
(6) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9142.5 to clear it?
(7) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $7332 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 10% simple interest.
(9) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 10% simple interest.
(10) How much loan did Matthew borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7750 to clear it?