Question:
If Anthony paid $4988 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
Correct Answer
$4300
Solution And Explanation
Solution
Given,
Amount (A) = $4988
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
$4988 = P (1 + 4% × 4)
⇒ $4988 = P (1 + 4/100 × 4)
⇒ $4988 = P (1 + 4 × 4/100)
⇒ $4988 = P (1 + 16/100)
⇒ $4988 = P (100 + 16/100)
⇒ $4988 = P × 116/100
⇒ P × 116/100 = $4988
⇒ P = 4988/116/100
⇒ P = 4988 × 100/116
⇒ P = 4988 × 100/116
⇒ P = 498800/116
⇒ P = $4300
Thus, the sum borrowed (P) = $4300 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 4988, then the Principal = 100/116 × 4988
= 100 × 4988/116
= 498800/116
= 4300
Thus, Principal = $4300
Thus, the sum borrowed = $4300 Answer
Similar Questions
(1) Robert had to pay $3379 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(2) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 9% simple interest?
(3) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $9204 to clear the loan, then find the time period of the loan.
(4) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $8772 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if William borrowed a sum of $3500 at 6% simple interest for 4 years.
(6) How much loan did Ryan borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8690 to clear it?
(7) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 10% simple interest?
(8) In how much time a principal of $3000 will amount to $3240 at a simple interest of 4% per annum?
(9) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 9% simple interest?
(10) What amount will be due after 2 years if David borrowed a sum of $3200 at a 6% simple interest?