Question:
Donna had to pay $5141 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
$4850
Solution And Explanation
Solution
Given,
Amount (A) = $5141
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
$5141 = P (1 + 2% × 3)
⇒ $5141 = P (1 + 2/100 × 3)
⇒ $5141 = P (1 + 2 × 3/100)
⇒ $5141 = P (1 + 6/100)
⇒ $5141 = P (100 + 6/100)
⇒ $5141 = P × 106/100
⇒ P × 106/100 = $5141
⇒ P = 5141/106/100
⇒ P = 5141 × 100/106
⇒ P = 5141 × 100/106
⇒ P = 514100/106
⇒ 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 = 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 5141, then the Principal = 100/106 × 5141
= 100 × 5141/106
= 514100/106
= 4850
Thus, Principal = $4850
Thus, the sum borrowed = $4850 Answer
Similar Questions
(1) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $7740 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 2% simple interest.
(3) Calculate the amount due if Jessica borrowed a sum of $3750 at 6% simple interest for 4 years.
(4) Calculate the amount due if Christopher borrowed a sum of $4000 at 3% simple interest for 3 years.
(5) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $7990 to clear the loan, then find the time period of the loan.
(6) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $9231 to clear the loan, then find the time period of the loan.
(7) How much loan did Edward borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9500 to clear it?
(8) Betty had to pay $4505 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(9) If Robert paid $3472 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(10) If Christopher paid $4640 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.