Question:
Donna had to pay $5286.5 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
$4850
Solution And Explanation
Solution
Given,
Amount (A) = $5286.5
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
$5286.5 = P (1 + 3% × 3)
⇒ $5286.5 = P (1 + 3/100 × 3)
⇒ $5286.5 = P (1 + 3 × 3/100)
⇒ $5286.5 = P (1 + 9/100)
⇒ $5286.5 = P (100 + 9/100)
⇒ $5286.5 = P × 109/100
⇒ P × 109/100 = $5286.5
⇒ P = 5286.5/109/100
⇒ P = 5286.5 × 100/109
⇒ P = 5286.5 × 100/109
⇒ P = 528650/109
⇒ P = $4850
Thus, the sum borrowed (P) = $4850 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 5286.5, then the Principal = 100/109 × 5286.5
= 100 × 5286.5/109
= 528650/109
= 4850
Thus, Principal = $4850
Thus, the sum borrowed = $4850 Answer
Similar Questions
(1) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $9500 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 7% simple interest.
(3) Find the amount to be paid if Barbara borrowed a sum of $5550 at 9% simple interest for 7 years.
(4) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $6800 to clear the loan, then find the time period of the loan.
(5) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $7052 to clear the loan, then find the time period of the loan.
(6) Patricia had to pay $3622.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(7) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 2% simple interest.
(8) Thomas had to pay $4256 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(9) If Mark paid $5104 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(10) Find the amount to be paid if David borrowed a sum of $5400 at 8% simple interest for 8 years.