Question:
Daniel had to pay $4469 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
$4100
Solution And Explanation
Solution
Given,
Amount (A) = $4469
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
$4469 = P (1 + 3% × 3)
⇒ $4469 = P (1 + 3/100 × 3)
⇒ $4469 = P (1 + 3 × 3/100)
⇒ $4469 = P (1 + 9/100)
⇒ $4469 = P (100 + 9/100)
⇒ $4469 = P × 109/100
⇒ P × 109/100 = $4469
⇒ P = 4469/109/100
⇒ P = 4469 × 100/109
⇒ P = 4469 × 100/109
⇒ P = 446900/109
⇒ P = $4100
Thus, the sum borrowed (P) = $4100 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 4469, then the Principal = 100/109 × 4469
= 100 × 4469/109
= 446900/109
= 4100
Thus, Principal = $4100
Thus, the sum borrowed = $4100 Answer
Similar Questions
(1) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 3% simple interest for 3 years.
(2) In how much time a principal of $3050 will amount to $3233 at a simple interest of 2% per annum?
(3) Find the amount to be paid if David borrowed a sum of $5400 at 10% simple interest for 8 years.
(4) Calculate the amount due if Linda borrowed a sum of $3350 at 7% simple interest for 3 years.
(5) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $9200 to clear the loan, then find the time period of the loan.
(6) If Daniel paid $4920 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(7) In how much time a principal of $3050 will amount to $3416 at a simple interest of 4% per annum?
(8) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $10317 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Joseph borrowed a sum of $3700 at 4% simple interest for 4 years.
(10) Find the amount to be paid if Barbara borrowed a sum of $5550 at 4% simple interest for 7 years.