Question:
Charles had to pay $4368 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
Correct Answer
$3900
Solution And Explanation
Solution
Given,
Amount (A) = $4368
Rate of Simple Interest (R) = 4%
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
$4368 = P (1 + 4% × 3)
⇒ $4368 = P (1 + 4/100 × 3)
⇒ $4368 = P (1 + 4 × 3/100)
⇒ $4368 = P (1 + 12/100)
⇒ $4368 = P (100 + 12/100)
⇒ $4368 = P × 112/100
⇒ P × 112/100 = $4368
⇒ P = 4368/112/100
⇒ P = 4368 × 100/112
⇒ P = 4368 × 100/112
⇒ P = 436800/112
⇒ P = $3900
Thus, the sum borrowed (P) = $3900 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 = 4% per annum
Thus, Interest = 4% of principal
⇒ Interest = 4% of 100 = 4
Thus, Simple Interest for 1 year = 4
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 × 4 = 12
Thus, simple interest for 3 years = 12
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 12 = 112
Calculation of the Principal
Now,
∵ If the Amount is 112, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/112
∴ If the Amount is 4368, then the Principal = 100/112 × 4368
= 100 × 4368/112
= 436800/112
= 3900
Thus, Principal = $3900
Thus, the sum borrowed = $3900 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 9% simple interest.
(2) Calculate the amount due if James borrowed a sum of $3000 at 4% simple interest for 4 years.
(3) Calculate the amount due if Patricia borrowed a sum of $3150 at 7% simple interest for 3 years.
(4) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $10070 to clear the loan, then find the time period of the loan.
(5) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $11040 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 10% simple interest.
(7) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 5% simple interest.
(8) Calculate the amount due if William borrowed a sum of $3500 at 7% simple interest for 3 years.
(9) If Linda paid $3886 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(10) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $10164 to clear the loan, then find the time period of the loan.