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) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $11403 to clear the loan, then find the time period of the loan.
(2) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $8778 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 4% simple interest.
(4) Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $10296 to clear the loan, then find the time period of the loan.
(5) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $10720 to clear the loan, then find the time period of the loan.
(6) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 6% simple interest?
(7) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 3% simple interest?
(8) Calculate the amount due if James borrowed a sum of $3000 at 5% simple interest for 3 years.
(9) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 10% simple interest.
(10) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 4% simple interest.