Question:
Joshua had to pay $5341 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
$4900
Solution And Explanation
Solution
Given,
Amount (A) = $5341
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
$5341 = P (1 + 3% × 3)
⇒ $5341 = P (1 + 3/100 × 3)
⇒ $5341 = P (1 + 3 × 3/100)
⇒ $5341 = P (1 + 9/100)
⇒ $5341 = P (100 + 9/100)
⇒ $5341 = P × 109/100
⇒ P × 109/100 = $5341
⇒ P = 5341/109/100
⇒ P = 5341 × 100/109
⇒ P = 5341 × 100/109
⇒ P = 534100/109
⇒ P = $4900
Thus, the sum borrowed (P) = $4900 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 5341, then the Principal = 100/109 × 5341
= 100 × 5341/109
= 534100/109
= 4900
Thus, Principal = $4900
Thus, the sum borrowed = $4900 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 8% simple interest.
(2) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Joseph borrowed a sum of $5700 at 10% simple interest for 7 years.
(4) In how much time a principal of $3050 will amount to $3294 at a simple interest of 2% per annum?
(5) Calculate the amount due if William borrowed a sum of $3500 at 2% simple interest for 3 years.
(6) If Matthew paid $4536 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(7) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 7% simple interest?
(8) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $12160 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 9% simple interest.
(10) What amount will be due after 2 years if James borrowed a sum of $3000 at a 7% simple interest?