Question:
Nancy had to pay $4399 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
$4150
Solution And Explanation
Solution
Given,
Amount (A) = $4399
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
$4399 = P (1 + 2% × 3)
⇒ $4399 = P (1 + 2/100 × 3)
⇒ $4399 = P (1 + 2 × 3/100)
⇒ $4399 = P (1 + 6/100)
⇒ $4399 = P (100 + 6/100)
⇒ $4399 = P × 106/100
⇒ P × 106/100 = $4399
⇒ P = 4399/106/100
⇒ P = 4399 × 100/106
⇒ P = 4399 × 100/106
⇒ P = 439900/106
⇒ P = $4150
Thus, the sum borrowed (P) = $4150 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 4399, then the Principal = 100/106 × 4399
= 100 × 4399/106
= 439900/106
= 4150
Thus, Principal = $4150
Thus, the sum borrowed = $4150 Answer
Similar Questions
(1) If Robert paid $3596 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(2) Calculate the amount due if Mary borrowed a sum of $3050 at 5% simple interest for 3 years.
(3) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $9916 to clear the loan, then find the time period of the loan.
(4) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $7360 to clear the loan, then find the time period of the loan.
(5) If Robert borrowed $3100 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(6) Find the amount to be paid if James borrowed a sum of $5000 at 4% simple interest for 7 years.
(7) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $10880 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Jennifer borrowed a sum of $3250 at 8% simple interest for 4 years.
(9) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6683 to clear the loan, then find the time period of the loan.
(10) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $7480 to clear the loan, then find the time period of the loan.