Question:
If Paul paid $5076 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
Correct Answer
$4700
Solution And Explanation
Solution
Given,
Amount (A) = $5076
Rate of Simple Interest (R) = 2%
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
$5076 = P (1 + 2% × 4)
⇒ $5076 = P (1 + 2/100 × 4)
⇒ $5076 = P (1 + 2 × 4/100)
⇒ $5076 = P (1 + 8/100)
⇒ $5076 = P (100 + 8/100)
⇒ $5076 = P × 108/100
⇒ P × 108/100 = $5076
⇒ P = 5076/108/100
⇒ P = 5076 × 100/108
⇒ P = 5076 × 100/108
⇒ P = 507600/108
⇒ P = $4700
Thus, the sum borrowed (P) = $4700 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 = 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 × 2 = 8
Thus, simple interest for 4 years = 8
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 8 = 108
Calculation of the Principal
Now,
∵ If the Amount is 108, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/108
∴ If the Amount is 5076, then the Principal = 100/108 × 5076
= 100 × 5076/108
= 507600/108
= 4700
Thus, Principal = $4700
Thus, the sum borrowed = $4700 Answer
Similar Questions
(1) Calculate the amount due if William borrowed a sum of $3500 at 4% simple interest for 3 years.
(2) If David paid $3944 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(3) Calculate the amount due if David borrowed a sum of $3400 at 7% simple interest for 3 years.
(4) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 6% simple interest?
(5) If Robert paid $3472 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(6) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 3% simple interest.
(7) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $11780 to clear the loan, then find the time period of the loan.
(8) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $10317 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 8% simple interest for 4 years.
(10) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 5% simple interest.