Question:
How much loan did Andrew borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7480 to clear it?
Correct Answer
$6800
Solution And Explanation
Solution
Given,
Amount (A) = $7480
Rate of Simple Interest (R) = 2%
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
$7480 = P (1 + 2% × 5)
⇒ $7480 = P (1 + 2/100 × 5)
⇒ $7480 = P (1 + 2 × 5/100)
⇒ $7480 = P (1 + 10/100)
⇒ $7480 = P (100 + 10/100)
⇒ $7480 = P × 110/100
⇒ P × 110/100 = $7480
⇒ P = 7480/110/100
⇒ P = 7480 × 100/110
⇒ P = 7480 × 100/110
⇒ P = 748000/110
⇒ P = $6800
Thus, the sum borrowed (P) = $6800 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 = 2% per annum
Thus, Interest = 2% of principal
⇒ Interest = 2% of 100 = 2
Thus, Simple Interest for 1 year = 2
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 × 2 = 10
Thus, simple interest for 5 years = 10
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 10 = 110
Calculation of the Principal
Now,
∵ If the Amount is 110, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/110
∴ If the Amount is 7480, then the Principal = 100/110 × 7480
= 100 × 7480/110
= 748000/110
= 6800
Thus, Principal = $6800
Thus, the sum borrowed = $6800 Answer
Similar Questions
(1) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $10432 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Mary borrowed a sum of $5050 at 2% simple interest for 7 years.
(3) Calculate the amount due if Mary borrowed a sum of $3050 at 9% simple interest for 3 years.
(4) How much loan did William borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6875 to clear it?
(5) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 10% simple interest.
(6) Calculate the amount due if Joseph borrowed a sum of $3700 at 6% simple interest for 4 years.
(7) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $8008 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 7% simple interest.
(9) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 3% simple interest.