Question:
James had to pay $3270 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
$3000
Solution And Explanation
Solution
Given,
Amount (A) = $3270
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
$3270 = P (1 + 3% × 3)
⇒ $3270 = P (1 + 3/100 × 3)
⇒ $3270 = P (1 + 3 × 3/100)
⇒ $3270 = P (1 + 9/100)
⇒ $3270 = P (100 + 9/100)
⇒ $3270 = P × 109/100
⇒ P × 109/100 = $3270
⇒ P = 3270/109/100
⇒ P = 3270 × 100/109
⇒ P = 3270 × 100/109
⇒ P = 327000/109
⇒ P = $3000
Thus, the sum borrowed (P) = $3000 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 3270, then the Principal = 100/109 × 3270
= 100 × 3270/109
= 327000/109
= 3000
Thus, Principal = $3000
Thus, the sum borrowed = $3000 Answer
Similar Questions
(1) Find the amount to be paid if Sarah borrowed a sum of $5850 at 8% simple interest for 7 years.
(2) If Margaret paid $4698 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(3) Calculate the amount due if Sarah borrowed a sum of $3850 at 7% simple interest for 3 years.
(4) How much loan did Robert borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6375 to clear it?
(5) How much loan did Emily borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7425 to clear it?
(6) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 5% simple interest?
(7) What amount will be due after 2 years if William borrowed a sum of $3250 at a 10% simple interest?
(8) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 6% simple interest.
(9) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 3% simple interest.
(10) If Barbara paid $3976 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.