Question

Calculate the principal when time = 4 years, interest= Rs. 4,000 and rate= 10% per annum.
 (a) Rs. 5,000
 (b) Rs. 10,000
 (c) Rs. 15,000
 (d) Rs. 20,000

Answer 1

Hint: It is a word problem related to the money exchange. The only thing you need to focus on for solving this problem is the percentage calculation and must know the definition of simple interest.

Complete step-by-step answer:
Before starting with the question, let us know about interest.
Interest, in the financial term, is the amount that a borrower pays to the lender along with the repayment of the actual principal amount.
Broadly, there are two kinds of interest. First is the simple interest and the other is the compound interest.
Moving to the solution of the question.
Given:
Time = 4 years.
Rate = 10% per annum = $\dfrac{10}{100}$ per annum.
Total interest gained in 4 years = Rs. 4,000.
Let the principal be p.
Let the amount be a.
According to the definition of interest:
Amount = principal + interest.
$\therefore $ a = p + interest
Simple interest is mathematically defined as:
$\text{interest=principal }\!\!\times\!\!\text{ rate }\!\!\times\!\!\text{ time}\text{.}$
So, using the above formula, we get;
$4000=p\times \dfrac{10}{100}\times 4$
$\Rightarrow 4000=p\times \dfrac{1}{10}\times 4$
$\Rightarrow p=\dfrac{40000}{4}$
$\Rightarrow p=10000$
 The principal of the data given in the question comes out to be Rs. 10,000
Hence, the answer to the question is option (b) Rs. 10,000.

Note: Be careful if the interest mentioned in the question is simple or compound interest. Also, if nothing directly mentioned, you must know fixed deposits pay you compound interest, rest generally pay you simple interest against your deposit.