Question:
If Lisa paid $4860 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
Correct Answer
$4050
Solution And Explanation
Solution
Given,
Amount (A) = $4860
Rate of Simple Interest (R) = 5%
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
$4860 = P (1 + 5% × 4)
⇒ $4860 = P (1 + 5/100 × 4)
⇒ $4860 = P (1 + 5 × 4/100)
⇒ $4860 = P (1 + 20/100)
⇒ $4860 = P (100 + 20/100)
⇒ $4860 = P × 120/100
⇒ P × 120/100 = $4860
⇒ P = 4860/120/100
⇒ P = 4860 × 100/120
⇒ P = 4860 × 100/120
⇒ P = 486000/120
⇒ P = $4050
Thus, the sum borrowed (P) = $4050 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 = 5% per annum
Thus, Interest = 5% of principal
⇒ Interest = 5% of 100 = 5
Thus, Simple Interest for 1 year = 5
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 × 5 = 20
Thus, simple interest for 4 years = 20
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 20 = 120
Calculation of the Principal
Now,
∵ If the Amount is 120, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/120
∴ If the Amount is 4860, then the Principal = 100/120 × 4860
= 100 × 4860/120
= 486000/120
= 4050
Thus, Principal = $4050
Thus, the sum borrowed = $4050 Answer
Similar Questions
(1) If Lisa paid $4860 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(2) If Paul paid $5076 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(3) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 4% simple interest.
(4) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 9% simple interest?
(5) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $11247 to clear the loan, then find the time period of the loan.
(6) Matthew had to pay $4704 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(7) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 9% simple interest.
(9) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $7990 to clear the loan, then find the time period of the loan.
(10) If Elizabeth paid $3864 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.