Question:
Anthony had to pay $4945 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
$4300
Solution And Explanation
Solution
Given,
Amount (A) = $4945
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
$4945 = P (1 + 5% × 3)
⇒ $4945 = P (1 + 5/100 × 3)
⇒ $4945 = P (1 + 5 × 3/100)
⇒ $4945 = P (1 + 15/100)
⇒ $4945 = P (100 + 15/100)
⇒ $4945 = P × 115/100
⇒ P × 115/100 = $4945
⇒ P = 4945/115/100
⇒ P = 4945 × 100/115
⇒ P = 4945 × 100/115
⇒ P = 494500/115
⇒ P = $4300
Thus, the sum borrowed (P) = $4300 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 4945, then the Principal = 100/115 × 4945
= 100 × 4945/115
= 494500/115
= 4300
Thus, Principal = $4300
Thus, the sum borrowed = $4300 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 5% simple interest.
(2) In how much time a principal of $3000 will amount to $3300 at a simple interest of 2% per annum?
(3) Calculate the amount due if Susan borrowed a sum of $3650 at 2% simple interest for 3 years.
(4) How much loan did Barbara borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6382.5 to clear it?
(5) In how much time a principal of $3050 will amount to $3660 at a simple interest of 4% per annum?
(6) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 7% simple interest?
(7) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $10626 to clear the loan, then find the time period of the loan.
(8) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 7% simple interest?
(9) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 7% simple interest.
(10) Calculate the amount due if Richard borrowed a sum of $3600 at 9% simple interest for 4 years.