Question:
Sarah had to pay $4196.5 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
$3850
Solution And Explanation
Solution
Given,
Amount (A) = $4196.5
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
$4196.5 = P (1 + 3% × 3)
⇒ $4196.5 = P (1 + 3/100 × 3)
⇒ $4196.5 = P (1 + 3 × 3/100)
⇒ $4196.5 = P (1 + 9/100)
⇒ $4196.5 = P (100 + 9/100)
⇒ $4196.5 = P × 109/100
⇒ P × 109/100 = $4196.5
⇒ P = 4196.5/109/100
⇒ P = 4196.5 × 100/109
⇒ P = 4196.5 × 100/109
⇒ P = 419650/109
⇒ P = $3850
Thus, the sum borrowed (P) = $3850 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 4196.5, then the Principal = 100/109 × 4196.5
= 100 × 4196.5/109
= 419650/109
= 3850
Thus, Principal = $3850
Thus, the sum borrowed = $3850 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 8% simple interest.
(2) Find the amount to be paid if Robert borrowed a sum of $5100 at 2% simple interest for 7 years.
(3) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $7335 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 4% simple interest.
(5) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 7% simple interest.
(6) How much loan did Laura borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9812.5 to clear it?
(7) Calculate the amount due if Sarah borrowed a sum of $3850 at 2% simple interest for 3 years.
(8) How much loan did Ryan borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9085 to clear it?
(9) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 9% simple interest?
(10) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $8568 to clear the loan, then find the time period of the loan.