Question:
Daniel had to pay $4469 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
Correct Answer
$4100
Solution And Explanation
Solution
Given,
Amount (A) = $4469
Rate of Simple Interest (R) = 3%
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
$4469 = P (1 + 3% × 3)
⇒ $4469 = P (1 + 3/100 × 3)
⇒ $4469 = P (1 + 3 × 3/100)
⇒ $4469 = P (1 + 9/100)
⇒ $4469 = P (100 + 9/100)
⇒ $4469 = P × 109/100
⇒ P × 109/100 = $4469
⇒ P = 4469/109/100
⇒ P = 4469 × 100/109
⇒ P = 4469 × 100/109
⇒ P = 446900/109
⇒ P = $4100
Thus, the sum borrowed (P) = $4100 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 = 3% per annum
Thus, Interest = 3% of principal
⇒ Interest = 3% of 100 = 3
Thus, Simple Interest for 1 year = 3
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 × 3 = 9
Thus, simple interest for 3 years = 9
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 9 = 109
Calculation of the Principal
Now,
∵ If the Amount is 109, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/109
∴ If the Amount is 4469, then the Principal = 100/109 × 4469
= 100 × 4469/109
= 446900/109
= 4100
Thus, Principal = $4100
Thus, the sum borrowed = $4100 Answer
Similar Questions
(1) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $6520 to clear the loan, then find the time period of the loan.
(2) In how much time a principal of $3200 will amount to $3392 at a simple interest of 2% per annum?
(3) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 9% simple interest.
(4) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $8520 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Sarah borrowed a sum of $5850 at 2% simple interest for 8 years.
(6) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $6468 to clear the loan, then find the time period of the loan.
(7) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $9880 to clear the loan, then find the time period of the loan.
(8) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $11780 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 2% simple interest.
(10) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $10064 to clear the loan, then find the time period of the loan.