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) Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $11352 to clear the loan, then find the time period of the loan.
(2) What amount will be due after 2 years if John borrowed a sum of $3100 at a 7% simple interest?
(3) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 7% simple interest?
(4) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 7% simple interest?
(5) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 10% simple interest.
(6) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 5% simple interest?
(7) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $5440 to clear the loan, then find the time period of the loan.
(8) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $9324 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 9% simple interest.
(10) How much loan did Edward borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8740 to clear it?