Question:
( 1 of 10 ) If William paid $3780 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(A) $6750
(B) $5400
(C) $8100
(D) $8424
You selected
$2835
Correct Answer
$3500
Solution And Explanation
Solution
Given,
Amount (A) = $3780
Rate of Simple Interest (R) = 2%
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
$3780 = P (1 + 2% × 4)
⇒ $3780 = P (1 + 2/100 × 4)
⇒ $3780 = P (1 + 2 × 4/100)
⇒ $3780 = P (1 + 8/100)
⇒ $3780 = P (100 + 8/100)
⇒ $3780 = P × 108/100
⇒ P × 108/100 = $3780
⇒ P = 3780/108/100
⇒ P = 3780 × 100/108
⇒ P = 3780 × 100/108
⇒ P = 378000/108
⇒ 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 = 2% per annum
Thus, Interest = 2% of principal
⇒ Interest = 2% of 100 = 2
Thus, Simple Interest for 1 year = 2
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 × 2 = 8
Thus, simple interest for 4 years = 8
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 8 = 108
Calculation of the Principal
Now,
∵ If the Amount is 108, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/108
∴ If the Amount is 3780, then the Principal = 100/108 × 3780
= 100 × 3780/108
= 378000/108
= 3500
Thus, Principal = $3500
Thus, the sum borrowed = $3500 Answer