Question:
How much loan did Christopher borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7200 to clear it?
Correct Answer
$6000
Solution And Explanation
Solution
Given,
Amount (A) = $7200
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
$7200 = P (1 + 4% × 5)
⇒ $7200 = P (1 + 4/100 × 5)
⇒ $7200 = P (1 + 4 × 5/100)
⇒ $7200 = P (1 + 20/100)
⇒ $7200 = P (100 + 20/100)
⇒ $7200 = P × 120/100
⇒ P × 120/100 = $7200
⇒ P = 7200/120/100
⇒ P = 7200 × 100/120
⇒ P = 7200 × 100/120
⇒ P = 720000/120
⇒ P = $6000
Thus, the sum borrowed (P) = $6000 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 7200, then the Principal = 100/120 × 7200
= 100 × 7200/120
= 720000/120
= 6000
Thus, Principal = $6000
Thus, the sum borrowed = $6000 Answer
Similar Questions
(1) Find the amount to be paid if Barbara borrowed a sum of $5550 at 3% simple interest for 8 years.
(2) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $10269 to clear the loan, then find the time period of the loan.
(3) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $10980 to clear the loan, then find the time period of the loan.
(4) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $8800 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 7% simple interest.
(6) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $12060 to clear the loan, then find the time period of the loan.
(7) Thomas took a loan of $5600 at the rate of 7% simple interest per annum. If he paid an amount of $7952 to clear the loan, then find the time period of the loan.
(8) Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $6392 to clear the loan, then find the time period of the loan.
(9) How much loan did Elizabeth borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6812.5 to clear it?
(10) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $7700 to clear the loan, then find the time period of the loan.