Question:
Anthony had to pay $4687 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
$4300
Solution And Explanation
Solution
Given,
Amount (A) = $4687
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
$4687 = P (1 + 3% × 3)
⇒ $4687 = P (1 + 3/100 × 3)
⇒ $4687 = P (1 + 3 × 3/100)
⇒ $4687 = P (1 + 9/100)
⇒ $4687 = P (100 + 9/100)
⇒ $4687 = P × 109/100
⇒ P × 109/100 = $4687
⇒ P = 4687/109/100
⇒ P = 4687 × 100/109
⇒ P = 4687 × 100/109
⇒ P = 468700/109
⇒ 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 = 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 4687, then the Principal = 100/109 × 4687
= 100 × 4687/109
= 468700/109
= 4300
Thus, Principal = $4300
Thus, the sum borrowed = $4300 Answer
Similar Questions
(1) In how much time a principal of $3050 will amount to $3507.5 at a simple interest of 3% per annum?
(2) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 8% simple interest?
(3) Find the amount to be paid if James borrowed a sum of $5000 at 10% simple interest for 7 years.
(4) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $6560 to clear the loan, then find the time period of the loan.
(5) If Patricia paid $3528 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(6) In how much time a principal of $3050 will amount to $3233 at a simple interest of 2% per annum?
(7) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $9128 to clear the loan, then find the time period of the loan.
(8) How much loan did Sandra borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7095 to clear it?
(9) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 10% simple interest.
(10) Robert had to pay $3286 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.