Question:
Sandra had to pay $4717 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
$4450
Solution And Explanation
Solution
Given,
Amount (A) = $4717
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
$4717 = P (1 + 2% × 3)
⇒ $4717 = P (1 + 2/100 × 3)
⇒ $4717 = P (1 + 2 × 3/100)
⇒ $4717 = P (1 + 6/100)
⇒ $4717 = P (100 + 6/100)
⇒ $4717 = P × 106/100
⇒ P × 106/100 = $4717
⇒ P = 4717/106/100
⇒ P = 4717 × 100/106
⇒ P = 4717 × 100/106
⇒ P = 471700/106
⇒ 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 = 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 4717, then the Principal = 100/106 × 4717
= 100 × 4717/106
= 471700/106
= 4450
Thus, Principal = $4450
Thus, the sum borrowed = $4450 Answer
Similar Questions
(1) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 7% simple interest?
(2) Find the amount to be paid if Jessica borrowed a sum of $5750 at 9% simple interest for 7 years.
(3) Find the amount to be paid if Jessica borrowed a sum of $5750 at 3% simple interest for 8 years.
(4) Calculate the amount due if Karen borrowed a sum of $3950 at 4% simple interest for 4 years.
(5) In how much time a principal of $3150 will amount to $3465 at a simple interest of 2% per annum?
(6) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 10% simple interest?
(7) How much loan did Jacob borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $10000 to clear it?
(8) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $13300 to clear the loan, then find the time period of the loan.
(9) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $9010 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if William borrowed a sum of $3500 at 8% simple interest for 4 years.