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 Jessica paid $4050 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(2) Find the amount to be paid if Mary borrowed a sum of $5050 at 4% simple interest for 8 years.
(3) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 10% simple interest?
(4) Calculate the amount due if David borrowed a sum of $3400 at 5% simple interest for 4 years.
(5) 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.
(6) If Michelle paid $5940 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(7) 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.
(8) Find the amount to be paid if Charles borrowed a sum of $5900 at 6% simple interest for 7 years.
(9) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 6% simple interest?
(10) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $7335 to clear the loan, then find the time period of the loan.