Question:
Michael had to pay $3795 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
$3300
Solution And Explanation
Solution
Given,
Amount (A) = $3795
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
$3795 = P (1 + 5% × 3)
⇒ $3795 = P (1 + 5/100 × 3)
⇒ $3795 = P (1 + 5 × 3/100)
⇒ $3795 = P (1 + 15/100)
⇒ $3795 = P (100 + 15/100)
⇒ $3795 = P × 115/100
⇒ P × 115/100 = $3795
⇒ P = 3795/115/100
⇒ P = 3795 × 100/115
⇒ P = 3795 × 100/115
⇒ P = 379500/115
⇒ P = $3300
Thus, the sum borrowed (P) = $3300 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 3795, then the Principal = 100/115 × 3795
= 100 × 3795/115
= 379500/115
= 3300
Thus, Principal = $3300
Thus, the sum borrowed = $3300 Answer
Similar Questions
(1) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $9387 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if James borrowed a sum of $5000 at 2% simple interest for 8 years.
(3) Find the amount to be paid if Sarah borrowed a sum of $5850 at 9% simple interest for 8 years.
(4) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $7332 to clear the loan, then find the time period of the loan.
(5) In how much time a principal of $3150 will amount to $3654 at a simple interest of 4% per annum?
(6) If Mark paid $5280 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(7) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 9% simple interest?
(8) In how much time a principal of $3150 will amount to $3465 at a simple interest of 5% per annum?
(9) Calculate the amount due if Mary borrowed a sum of $3050 at 6% simple interest for 3 years.
(10) Find the amount to be paid if Mary borrowed a sum of $5050 at 6% simple interest for 8 years.