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 if Elizabeth borrowed a sum of $3450 at 4% simple interest for 4 years.
(2) Find the amount to be paid if Jessica borrowed a sum of $5750 at 3% simple interest for 8 years.
(3) Calculate the amount due if Thomas borrowed a sum of $3800 at 3% simple interest for 4 years.
(4) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $7680 to clear the loan, then find the time period of the loan.
(5) What amount does John have to pay after 5 years if he takes a loan of $3200 at 7% simple interest?
(6) Find the amount to be paid if Patricia borrowed a sum of $5150 at 10% simple interest for 7 years.
(7) Find the amount to be paid if James borrowed a sum of $5000 at 2% simple interest for 8 years.
(8) How much loan did Carol borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7755 to clear it?
(9) Calculate the amount due if William borrowed a sum of $3500 at 10% simple interest for 4 years.
(10) How much loan did Mark borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7040 to clear it?