Question:
How much loan did George borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8760 to clear it?
Correct Answer
$7300
Solution And Explanation
Solution
Given,
Amount (A) = $8760
Rate of Simple Interest (R) = 4%
Time (T) = 5 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
$8760 = P (1 + 4% × 5)
⇒ $8760 = P (1 + 4/100 × 5)
⇒ $8760 = P (1 + 4 × 5/100)
⇒ $8760 = P (1 + 20/100)
⇒ $8760 = P (100 + 20/100)
⇒ $8760 = P × 120/100
⇒ P × 120/100 = $8760
⇒ P = 8760/120/100
⇒ P = 8760 × 100/120
⇒ P = 8760 × 100/120
⇒ P = 876000/120
⇒ P = $7300
Thus, the sum borrowed (P) = $7300 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 = 4% per annum
Thus, Interest = 4% of principal
⇒ Interest = 4% of 100 = 4
Thus, Simple Interest for 1 year = 4
Calculation of the Amount
Since, in the question, time = 5 years
So, we need to calculate the simple interest for the given time period, which is 5 years
Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year
= 5 × 4 = 20
Thus, simple interest for 5 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 8760, then the Principal = 100/120 × 8760
= 100 × 8760/120
= 876000/120
= 7300
Thus, Principal = $7300
Thus, the sum borrowed = $7300 Answer
Similar Questions
(1) What amount does John have to pay after 5 years if he takes a loan of $3200 at 10% simple interest?
(2) Calculate the amount due if Thomas borrowed a sum of $3800 at 9% simple interest for 4 years.
(3) If Christopher paid $4640 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(4) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 9% simple interest?
(5) Find the amount to be paid if Robert borrowed a sum of $5100 at 5% simple interest for 8 years.
(6) If William borrowed $3500 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(7) What amount does David have to pay after 5 years if he takes a loan of $3400 at 3% simple interest?
(8) Find the amount to be paid if Christopher borrowed a sum of $6000 at 2% simple interest for 7 years.
(9) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 5% simple interest?
(10) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 8% simple interest?