Question:
Susan had to pay $3869 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
$3650
Solution And Explanation
Solution
Given,
Amount (A) = $3869
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
$3869 = P (1 + 2% × 3)
⇒ $3869 = P (1 + 2/100 × 3)
⇒ $3869 = P (1 + 2 × 3/100)
⇒ $3869 = P (1 + 6/100)
⇒ $3869 = P (100 + 6/100)
⇒ $3869 = P × 106/100
⇒ P × 106/100 = $3869
⇒ P = 3869/106/100
⇒ P = 3869 × 100/106
⇒ P = 3869 × 100/106
⇒ P = 386900/106
⇒ P = $3650
Thus, the sum borrowed (P) = $3650 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 3869, then the Principal = 100/106 × 3869
= 100 × 3869/106
= 386900/106
= 3650
Thus, Principal = $3650
Thus, the sum borrowed = $3650 Answer
Similar Questions
(1) Calculate the amount due if Karen borrowed a sum of $3950 at 8% simple interest for 3 years.
(2) Find the amount to be paid if Jessica borrowed a sum of $5750 at 5% simple interest for 7 years.
(3) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $7740 to clear the loan, then find the time period of the loan.
(4) In how much time a principal of $3200 will amount to $3680 at a simple interest of 3% per annum?
(5) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 2% simple interest.
(6) Calculate the amount due if James borrowed a sum of $3000 at 5% simple interest for 4 years.
(7) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 2% simple interest for 3 years.
(8) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 9% simple interest?
(9) Christopher had to pay $4480 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(10) In how much time a principal of $3150 will amount to $3528 at a simple interest of 3% per annum?