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) How much loan did Stephanie borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8305 to clear it?
(2) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $10836 to clear the loan, then find the time period of the loan.
(3) 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.
(4) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 4% simple interest for 8 years.
(5) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $8280 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if Michael borrowed a sum of $3300 at 9% simple interest for 3 years.
(7) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 6% simple interest?
(8) If Steven paid $4968 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(9) If Linda paid $3618 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(10) Calculate the amount due if Patricia borrowed a sum of $3150 at 9% simple interest for 3 years.