Question:
If Charles paid $4524 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
Correct Answer
$3900
Solution And Explanation
Solution
Given,
Amount (A) = $4524
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
$4524 = P (1 + 4% × 4)
⇒ $4524 = P (1 + 4/100 × 4)
⇒ $4524 = P (1 + 4 × 4/100)
⇒ $4524 = P (1 + 16/100)
⇒ $4524 = P (100 + 16/100)
⇒ $4524 = P × 116/100
⇒ P × 116/100 = $4524
⇒ P = 4524/116/100
⇒ P = 4524 × 100/116
⇒ P = 4524 × 100/116
⇒ P = 452400/116
⇒ P = $3900
Thus, the sum borrowed (P) = $3900 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 4524, then the Principal = 100/116 × 4524
= 100 × 4524/116
= 452400/116
= 3900
Thus, Principal = $3900
Thus, the sum borrowed = $3900 Answer
Similar Questions
(1) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $11584 to clear the loan, then find the time period of the loan.
(2) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $8470 to clear the loan, then find the time period of the loan.
(3) If Joshua paid $5488 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(4) Calculate the amount due if Charles borrowed a sum of $3900 at 5% simple interest for 3 years.
(5) If Karen paid $4424 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(6) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $7987 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 5% simple interest.
(8) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 8% simple interest?
(9) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 4% simple interest?
(10) Calculate the amount due if Susan borrowed a sum of $3650 at 2% simple interest for 3 years.