Question:
If William paid $3920 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
Correct Answer
$3500
Solution And Explanation
Solution
Given,
Amount (A) = $3920
Rate of Simple Interest (R) = 3%
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
$3920 = P (1 + 3% × 4)
⇒ $3920 = P (1 + 3/100 × 4)
⇒ $3920 = P (1 + 3 × 4/100)
⇒ $3920 = P (1 + 12/100)
⇒ $3920 = P (100 + 12/100)
⇒ $3920 = P × 112/100
⇒ P × 112/100 = $3920
⇒ P = 3920/112/100
⇒ P = 3920 × 100/112
⇒ P = 3920 × 100/112
⇒ P = 392000/112
⇒ P = $3500
Thus, the sum borrowed (P) = $3500 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 = 3% per annum
Thus, Interest = 3% of principal
⇒ Interest = 3% of 100 = 3
Thus, Simple Interest for 1 year = 3
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 × 3 = 12
Thus, simple interest for 4 years = 12
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 12 = 112
Calculation of the Principal
Now,
∵ If the Amount is 112, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/112
∴ If the Amount is 3920, then the Principal = 100/112 × 3920
= 100 × 3920/112
= 392000/112
= 3500
Thus, Principal = $3500
Thus, the sum borrowed = $3500 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 7% simple interest.
(2) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $7824 to clear the loan, then find the time period of the loan.
(3) How much loan did Edward borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9500 to clear it?
(4) Find the amount to be paid if Jessica borrowed a sum of $5750 at 2% simple interest for 7 years.
(5) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 8% simple interest.
(6) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $9920 to clear the loan, then find the time period of the loan.
(7) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $8256 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 10% simple interest.
(9) 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.
(10) Find the amount to be paid if James borrowed a sum of $5000 at 10% simple interest for 7 years.