Question:
Sandra had to pay $4850.5 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
$4450
Solution And Explanation
Solution
Given,
Amount (A) = $4850.5
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
$4850.5 = P (1 + 3% × 3)
⇒ $4850.5 = P (1 + 3/100 × 3)
⇒ $4850.5 = P (1 + 3 × 3/100)
⇒ $4850.5 = P (1 + 9/100)
⇒ $4850.5 = P (100 + 9/100)
⇒ $4850.5 = P × 109/100
⇒ P × 109/100 = $4850.5
⇒ P = 4850.5/109/100
⇒ P = 4850.5 × 100/109
⇒ P = 4850.5 × 100/109
⇒ P = 485050/109
⇒ P = $4450
Thus, the sum borrowed (P) = $4450 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 4850.5, then the Principal = 100/109 × 4850.5
= 100 × 4850.5/109
= 485050/109
= 4450
Thus, Principal = $4450
Thus, the sum borrowed = $4450 Answer
Similar Questions
(1) How much loan did Donna borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7877.5 to clear it?
(2) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $6864 to clear the loan, then find the time period of the loan.
(3) How much loan did Michelle borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7645 to clear it?
(4) In how much time a principal of $3150 will amount to $3528 at a simple interest of 4% per annum?
(5) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $10450 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 9% simple interest for 7 years.
(7) Find the amount to be paid if Michael borrowed a sum of $5300 at 5% simple interest for 8 years.
(8) Calculate the amount due if Karen borrowed a sum of $3950 at 3% simple interest for 4 years.
(9) Calculate the amount due if William borrowed a sum of $3500 at 4% simple interest for 4 years.
(10) Calculate the amount due if Sarah borrowed a sum of $3850 at 9% simple interest for 4 years.