Question:
How much loan did Matthew borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7440 to clear it?
Correct Answer
$6200
Solution And Explanation
Solution
Given,
Amount (A) = $7440
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
$7440 = P (1 + 4% × 5)
⇒ $7440 = P (1 + 4/100 × 5)
⇒ $7440 = P (1 + 4 × 5/100)
⇒ $7440 = P (1 + 20/100)
⇒ $7440 = P (100 + 20/100)
⇒ $7440 = P × 120/100
⇒ P × 120/100 = $7440
⇒ P = 7440/120/100
⇒ P = 7440 × 100/120
⇒ P = 7440 × 100/120
⇒ P = 744000/120
⇒ P = $6200
Thus, the sum borrowed (P) = $6200 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 7440, then the Principal = 100/120 × 7440
= 100 × 7440/120
= 744000/120
= 6200
Thus, Principal = $6200
Thus, the sum borrowed = $6200 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 8% simple interest.
(2) Calculate the amount due if Robert borrowed a sum of $3100 at 4% simple interest for 4 years.
(3) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $10492 to clear the loan, then find the time period of the loan.
(4) If Matthew paid $4536 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(5) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $7052 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 4% simple interest.
(7) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $9120 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 6% simple interest.
(9) If Ashley paid $5278 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(10) How much loan did Donna borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8220 to clear it?