Question:
If David paid $4080 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
Correct Answer
$3400
Solution And Explanation
Solution
Given,
Amount (A) = $4080
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
$4080 = P (1 + 5% × 4)
⇒ $4080 = P (1 + 5/100 × 4)
⇒ $4080 = P (1 + 5 × 4/100)
⇒ $4080 = P (1 + 20/100)
⇒ $4080 = P (100 + 20/100)
⇒ $4080 = P × 120/100
⇒ P × 120/100 = $4080
⇒ P = 4080/120/100
⇒ P = 4080 × 100/120
⇒ P = 4080 × 100/120
⇒ P = 408000/120
⇒ P = $3400
Thus, the sum borrowed (P) = $3400 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 4080, then the Principal = 100/120 × 4080
= 100 × 4080/120
= 408000/120
= 3400
Thus, Principal = $3400
Thus, the sum borrowed = $3400 Answer
Similar Questions
(1) Calculate the amount due if Jessica borrowed a sum of $3750 at 5% simple interest for 3 years.
(2) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 10% simple interest?
(3) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 5% simple interest.
(4) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $7854 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 6% simple interest for 3 years.
(6) Calculate the amount due if Karen borrowed a sum of $3950 at 8% simple interest for 3 years.
(7) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 5% simple interest.
(8) If Margaret paid $5220 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(9) What amount will be due after 2 years if William borrowed a sum of $3250 at a 10% simple interest?
(10) Calculate the amount due if Robert borrowed a sum of $3100 at 6% simple interest for 4 years.