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) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $11970 to clear the loan, then find the time period of the loan.
(2) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $7790 to clear the loan, then find the time period of the loan.
(3) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 10% simple interest?
(4) Find the amount to be paid if Patricia borrowed a sum of $5150 at 7% simple interest for 7 years.
(5) If Ashley paid $4914 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(6) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 5% simple interest?
(7) Find the amount to be paid if Sarah borrowed a sum of $5850 at 9% simple interest for 7 years.
(8) How much loan did Christopher borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7200 to clear it?
(9) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $10920 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 4% simple interest.