Question:
If Matthew paid $5040 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
Correct Answer
$4200
Solution And Explanation
Solution
Given,
Amount (A) = $5040
Rate of Simple Interest (R) = 5%
Time (T) = 4 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
$5040 = P (1 + 5% × 4)
⇒ $5040 = P (1 + 5/100 × 4)
⇒ $5040 = P (1 + 5 × 4/100)
⇒ $5040 = P (1 + 20/100)
⇒ $5040 = P (100 + 20/100)
⇒ $5040 = P × 120/100
⇒ P × 120/100 = $5040
⇒ P = 5040/120/100
⇒ P = 5040 × 100/120
⇒ P = 5040 × 100/120
⇒ P = 504000/120
⇒ P = $4200
Thus, the sum borrowed (P) = $4200 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 = 4 years
So, we need to calculate the simple interest for the given time period, which is 4 years
Thus, Simple Interest for 4 years = 4 × Simple Interest for 1 year
= 4 × 5 = 20
Thus, simple interest for 4 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 5040, then the Principal = 100/120 × 5040
= 100 × 5040/120
= 504000/120
= 4200
Thus, Principal = $4200
Thus, the sum borrowed = $4200 Answer
Similar Questions
(1) Patricia had to pay $3528 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(2) Find the amount to be paid if Thomas borrowed a sum of $5800 at 6% simple interest for 7 years.
(3) Calculate the amount due if William borrowed a sum of $3500 at 8% simple interest for 3 years.
(4) Find the amount to be paid if Karen borrowed a sum of $5950 at 7% simple interest for 7 years.
(5) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 3% simple interest.
(6) If Mary paid $3416 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(7) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $9900 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Jessica borrowed a sum of $3750 at 2% simple interest for 3 years.
(9) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 7% simple interest?
(10) Calculate the amount due if Sarah borrowed a sum of $3850 at 8% simple interest for 4 years.