Question:
If James paid $3480 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
Correct Answer
$3000
Solution And Explanation
Solution
Given,
Amount (A) = $3480
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
$3480 = P (1 + 4% × 4)
⇒ $3480 = P (1 + 4/100 × 4)
⇒ $3480 = P (1 + 4 × 4/100)
⇒ $3480 = P (1 + 16/100)
⇒ $3480 = P (100 + 16/100)
⇒ $3480 = P × 116/100
⇒ P × 116/100 = $3480
⇒ P = 3480/116/100
⇒ P = 3480 × 100/116
⇒ P = 3480 × 100/116
⇒ P = 348000/116
⇒ P = $3000
Thus, the sum borrowed (P) = $3000 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 3480, then the Principal = 100/116 × 3480
= 100 × 3480/116
= 348000/116
= 3000
Thus, Principal = $3000
Thus, the sum borrowed = $3000 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 4% simple interest.
(2) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 7% simple interest?
(3) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 8% simple interest.
(4) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $6400 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 9% simple interest.
(6) Calculate the amount due if Thomas borrowed a sum of $3800 at 6% simple interest for 3 years.
(7) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 2% simple interest.
(8) Find the amount to be paid if Jessica borrowed a sum of $5750 at 8% simple interest for 8 years.
(9) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $6846 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if William borrowed a sum of $3500 at 2% simple interest for 4 years.