Question:
David had to pay $3910 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
Correct Answer
$3400
Solution And Explanation
Solution
Given,
Amount (A) = $3910
Rate of Simple Interest (R) = 5%
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
$3910 = P (1 + 5% × 3)
⇒ $3910 = P (1 + 5/100 × 3)
⇒ $3910 = P (1 + 5 × 3/100)
⇒ $3910 = P (1 + 15/100)
⇒ $3910 = P (100 + 15/100)
⇒ $3910 = P × 115/100
⇒ P × 115/100 = $3910
⇒ P = 3910/115/100
⇒ P = 3910 × 100/115
⇒ P = 3910 × 100/115
⇒ P = 391000/115
⇒ P = $3400
Thus, the sum borrowed (P) = $3400 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 = 5% per annum
Thus, Interest = 5% of principal
⇒ Interest = 5% of 100 = 5
Thus, Simple Interest for 1 year = 5
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 × 5 = 15
Thus, simple interest for 3 years = 15
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 15 = 115
Calculation of the Principal
Now,
∵ If the Amount is 115, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/115
∴ If the Amount is 3910, then the Principal = 100/115 × 3910
= 100 × 3910/115
= 391000/115
= 3400
Thus, Principal = $3400
Thus, the sum borrowed = $3400 Answer
Similar Questions
(1) In how much time a principal of $3100 will amount to $3472 at a simple interest of 4% per annum?
(2) What amount will be due after 2 years if John borrowed a sum of $3100 at a 9% simple interest?
(3) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $10030 to clear the loan, then find the time period of the loan.
(4) What amount does William have to pay after 5 years if he takes a loan of $3500 at 7% simple interest?
(5) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $8480 to clear the loan, then find the time period of the loan.
(6) If Barbara paid $3834 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(7) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 7% simple interest.
(8) If Joseph borrowed $3700 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(9) In how much time a principal of $3200 will amount to $3488 at a simple interest of 3% per annum?
(10) Calculate the amount due if David borrowed a sum of $3400 at 6% simple interest for 4 years.