Question:
Michael had to pay $3597 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
$3300
Solution And Explanation
Solution
Given,
Amount (A) = $3597
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
$3597 = P (1 + 3% × 3)
⇒ $3597 = P (1 + 3/100 × 3)
⇒ $3597 = P (1 + 3 × 3/100)
⇒ $3597 = P (1 + 9/100)
⇒ $3597 = P (100 + 9/100)
⇒ $3597 = P × 109/100
⇒ P × 109/100 = $3597
⇒ P = 3597/109/100
⇒ P = 3597 × 100/109
⇒ P = 3597 × 100/109
⇒ P = 359700/109
⇒ P = $3300
Thus, the sum borrowed (P) = $3300 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 3597, then the Principal = 100/109 × 3597
= 100 × 3597/109
= 359700/109
= 3300
Thus, Principal = $3300
Thus, the sum borrowed = $3300 Answer
Similar Questions
(1) Find the amount to be paid if Richard borrowed a sum of $5600 at 9% simple interest for 7 years.
(2) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 6% simple interest.
(3) Find the amount to be paid if Patricia borrowed a sum of $5150 at 4% simple interest for 7 years.
(4) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $10164 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 4% simple interest for 7 years.
(6) How much loan did Kenneth borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7700 to clear it?
(7) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 5% simple interest.
(8) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $10296 to clear the loan, then find the time period of the loan.
(9) How much loan did Ronald borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9375 to clear it?
(10) Calculate the amount due if William borrowed a sum of $3500 at 3% simple interest for 3 years.