Question:
If Andrew paid $5760 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
Correct Answer
$4800
Solution And Explanation
Solution
Given,
Amount (A) = $5760
Rate of Simple Interest (R) = 5%
Time (T) = 4 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
$5760 = P (1 + 5% × 4)
⇒ $5760 = P (1 + 5/100 × 4)
⇒ $5760 = P (1 + 5 × 4/100)
⇒ $5760 = P (1 + 20/100)
⇒ $5760 = P (100 + 20/100)
⇒ $5760 = P × 120/100
⇒ P × 120/100 = $5760
⇒ P = 5760/120/100
⇒ P = 5760 × 100/120
⇒ P = 5760 × 100/120
⇒ P = 576000/120
⇒ P = $4800
Thus, the sum borrowed (P) = $4800 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 = 4 years
So, we need to calculate the simple interest for the given time period, which is 4 years
Thus, Simple Interest for 4 years = 4 × Simple Interest for 1 year
= 4 × 5 = 20
Thus, simple interest for 4 years = 20
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 20 = 120
Calculation of the Principal
Now,
∵ If the Amount is 120, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/120
∴ If the Amount is 5760, then the Principal = 100/120 × 5760
= 100 × 5760/120
= 576000/120
= 4800
Thus, Principal = $4800
Thus, the sum borrowed = $4800 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 3% simple interest.
(2) Calculate the amount due if Charles borrowed a sum of $3900 at 5% simple interest for 4 years.
(3) Find the amount to be paid if William borrowed a sum of $5500 at 5% simple interest for 8 years.
(4) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 7% simple interest?
(5) Calculate the amount due if David borrowed a sum of $3400 at 5% simple interest for 3 years.
(6) Find the amount to be paid if Richard borrowed a sum of $5600 at 9% simple interest for 8 years.
(7) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $9204 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Susan borrowed a sum of $3650 at 4% simple interest for 3 years.
(9) Calculate the amount due if William borrowed a sum of $3500 at 4% simple interest for 3 years.
(10) In how much time a principal of $3100 will amount to $3286 at a simple interest of 3% per annum?