Question:
If Elizabeth paid $3864 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
Correct Answer
$3450
Solution And Explanation
Solution
Given,
Amount (A) = $3864
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
$3864 = P (1 + 3% × 4)
⇒ $3864 = P (1 + 3/100 × 4)
⇒ $3864 = P (1 + 3 × 4/100)
⇒ $3864 = P (1 + 12/100)
⇒ $3864 = P (100 + 12/100)
⇒ $3864 = P × 112/100
⇒ P × 112/100 = $3864
⇒ P = 3864/112/100
⇒ P = 3864 × 100/112
⇒ P = 3864 × 100/112
⇒ P = 386400/112
⇒ P = $3450
Thus, the sum borrowed (P) = $3450 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 3864, then the Principal = 100/112 × 3864
= 100 × 3864/112
= 386400/112
= 3450
Thus, Principal = $3450
Thus, the sum borrowed = $3450 Answer
Similar Questions
(1) 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.
(2) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $6160 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if John borrowed a sum of $3200 at 4% simple interest for 4 years.
(4) If Betty paid $4760 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(5) Calculate the amount due if Charles borrowed a sum of $3900 at 6% simple interest for 3 years.
(6) Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $11880 to clear the loan, then find the time period of the loan.
(7) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $10140 to clear the loan, then find the time period of the loan.
(8) In how much time a principal of $3100 will amount to $3875 at a simple interest of 5% per annum?
(9) Calculate the amount due if Joseph borrowed a sum of $3700 at 7% simple interest for 3 years.
(10) What amount will be due after 2 years if David borrowed a sum of $3200 at a 5% simple interest?