Question:
If Ashley paid $4914 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
Correct Answer
$4550
Solution And Explanation
Solution
Given,
Amount (A) = $4914
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
$4914 = P (1 + 2% × 4)
⇒ $4914 = P (1 + 2/100 × 4)
⇒ $4914 = P (1 + 2 × 4/100)
⇒ $4914 = P (1 + 8/100)
⇒ $4914 = P (100 + 8/100)
⇒ $4914 = P × 108/100
⇒ P × 108/100 = $4914
⇒ P = 4914/108/100
⇒ P = 4914 × 100/108
⇒ P = 4914 × 100/108
⇒ P = 491400/108
⇒ P = $4550
Thus, the sum borrowed (P) = $4550 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 4914, then the Principal = 100/108 × 4914
= 100 × 4914/108
= 491400/108
= 4550
Thus, Principal = $4550
Thus, the sum borrowed = $4550 Answer
Similar Questions
(1) If Charles paid $4368 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(2) Patricia had to pay $3433.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(3) In how much time a principal of $3150 will amount to $3937.5 at a simple interest of 5% per annum?
(4) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 10% simple interest for 7 years.
(5) Find the amount to be paid if James borrowed a sum of $5000 at 2% simple interest for 7 years.
(6) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $12160 to clear the loan, then find the time period of the loan.
(7) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $11400 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Richard borrowed a sum of $3600 at 3% simple interest for 3 years.
(9) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 8% simple interest?
(10) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 4% simple interest.