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) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $7252 to clear the loan, then find the time period of the loan.
(2) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 7% simple interest?
(3) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $9180 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Linda borrowed a sum of $5350 at 8% simple interest for 7 years.
(5) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 4% simple interest.
(6) How much loan did Ryan borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8690 to clear it?
(7) Find the amount to be paid if Susan borrowed a sum of $5650 at 10% simple interest for 8 years.
(8) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 9% simple interest.
(9) John had to pay $3680 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(10) In how much time a principal of $3150 will amount to $3780 at a simple interest of 4% per annum?