Question:
Margaret had to pay $4872 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
$4350
Solution And Explanation
Solution
Given,
Amount (A) = $4872
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
$4872 = P (1 + 4% × 3)
⇒ $4872 = P (1 + 4/100 × 3)
⇒ $4872 = P (1 + 4 × 3/100)
⇒ $4872 = P (1 + 12/100)
⇒ $4872 = P (100 + 12/100)
⇒ $4872 = P × 112/100
⇒ P × 112/100 = $4872
⇒ P = 4872/112/100
⇒ P = 4872 × 100/112
⇒ P = 4872 × 100/112
⇒ P = 487200/112
⇒ P = $4350
Thus, the sum borrowed (P) = $4350 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 4872, then the Principal = 100/112 × 4872
= 100 × 4872/112
= 487200/112
= 4350
Thus, Principal = $4350
Thus, the sum borrowed = $4350 Answer
Similar Questions
(1) Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $10540 to clear the loan, then find the time period of the loan.
(2) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $9180 to clear the loan, then find the time period of the loan.
(3) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $8800 to clear the loan, then find the time period of the loan.
(4) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $9086 to clear the loan, then find the time period of the loan.
(5) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $8960 to clear the loan, then find the time period of the loan.
(6) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $5920 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if Mary borrowed a sum of $3050 at 5% simple interest for 4 years.
(8) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Thomas borrowed a sum of $5800 at 10% simple interest for 7 years.
(10) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 6% simple interest.