Question:
How much loan did George borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9125 to clear it?
Correct Answer
$7300
Solution And Explanation
Solution
Given,
Amount (A) = $9125
Rate of Simple Interest (R) = 5%
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
$9125 = P (1 + 5% × 5)
⇒ $9125 = P (1 + 5/100 × 5)
⇒ $9125 = P (1 + 5 × 5/100)
⇒ $9125 = P (1 + 25/100)
⇒ $9125 = P (100 + 25/100)
⇒ $9125 = P × 125/100
⇒ P × 125/100 = $9125
⇒ P = 9125/125/100
⇒ P = 9125 × 100/125
⇒ P = 9125 × 100/125
⇒ P = 912500/125
⇒ 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 = 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 = 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 × 5 = 25
Thus, simple interest for 5 years = 25
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 25 = 125
Calculation of the Principal
Now,
∵ If the Amount is 125, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/125
∴ If the Amount is 9125, then the Principal = 100/125 × 9125
= 100 × 9125/125
= 912500/125
= 7300
Thus, Principal = $7300
Thus, the sum borrowed = $7300 Answer
Similar Questions
(1) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 7% simple interest?
(2) Calculate the amount due if Robert borrowed a sum of $3100 at 4% simple interest for 4 years.
(3) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $9000 to clear the loan, then find the time period of the loan.
(4) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $10260 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 2% simple interest for 7 years.
(6) Find the amount to be paid if Thomas borrowed a sum of $5800 at 2% simple interest for 8 years.
(7) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 3% simple interest for 8 years.
(8) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 9% simple interest.
(9) Calculate the amount due if Jessica borrowed a sum of $3750 at 9% simple interest for 4 years.
(10) Find the amount to be paid if James borrowed a sum of $5000 at 2% simple interest for 7 years.