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) Calculate the amount due if Christopher borrowed a sum of $4000 at 4% simple interest for 4 years.
(2) Calculate the amount due if Mary borrowed a sum of $3050 at 4% simple interest for 4 years.
(3) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $8170 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Karen borrowed a sum of $5950 at 5% simple interest for 8 years.
(5) Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $9280 to clear the loan, then find the time period of the loan.
(6) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 5% simple interest?
(7) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $11008 to clear the loan, then find the time period of the loan.
(8) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $8476 to clear the loan, then find the time period of the loan.
(9) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $11160 to clear the loan, then find the time period of the loan.
(10) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $9240 to clear the loan, then find the time period of the loan.