Question:
If Michael paid $3828 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
Correct Answer
$3300
Solution And Explanation
Solution
Given,
Amount (A) = $3828
Rate of Simple Interest (R) = 4%
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
$3828 = P (1 + 4% × 4)
⇒ $3828 = P (1 + 4/100 × 4)
⇒ $3828 = P (1 + 4 × 4/100)
⇒ $3828 = P (1 + 16/100)
⇒ $3828 = P (100 + 16/100)
⇒ $3828 = P × 116/100
⇒ P × 116/100 = $3828
⇒ P = 3828/116/100
⇒ P = 3828 × 100/116
⇒ P = 3828 × 100/116
⇒ P = 382800/116
⇒ P = $3300
Thus, the sum borrowed (P) = $3300 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 = 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 × 4 = 16
Thus, simple interest for 4 years = 16
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 16 = 116
Calculation of the Principal
Now,
∵ If the Amount is 116, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/116
∴ If the Amount is 3828, then the Principal = 100/116 × 3828
= 100 × 3828/116
= 382800/116
= 3300
Thus, Principal = $3300
Thus, the sum borrowed = $3300 Answer
Similar Questions
(1) Find the amount to be paid if William borrowed a sum of $5500 at 3% simple interest for 7 years.
(2) Calculate the amount due if Susan borrowed a sum of $3650 at 2% simple interest for 3 years.
(3) If Donald paid $4860 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(4) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $9440 to clear the loan, then find the time period of the loan.
(5) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $8869 to clear the loan, then find the time period of the loan.
(6) In how much time a principal of $3000 will amount to $3120 at a simple interest of 2% per annum?
(7) If Thomas paid $4560 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(8) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 3% simple interest?
(9) In how much time a principal of $3050 will amount to $3233 at a simple interest of 2% per annum?
(10) Calculate the amount due if Barbara borrowed a sum of $3550 at 4% simple interest for 3 years.