Final answer:
The correct annual interest rate that Sonika earned on her investment of Rs. 5,800 to get Rs. 6,394.5 after two years is approximately 5% per annum, option (A).
Step-by-step explanation:
To calculate the rate of compound interest for the amount invested by Sonika, we can use the formula for compound interest which is A = P(1 + r/n)^(nt), where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (decimal).
- n is the number of times that interest is compounded per year.
- t is the number of years the money is invested for.
Sonika invested Rs. 5,800 for 2 years and received a total of Rs. 6,394.5 after that period (Principal + Interest). We assume the interest is compounded annually (n=1), so our equation will look like 6,394.5 = 5,800(1 + r)^2. Solving for r gives us the annual interest rate Sonika earned on her investment.
First, let's divide both sides by the principal: 6,394.5 / 5,800 = (1 + r)^2. This simplifies to approximately 1.1025 = (1 + r)^2. Now, we take the square root of both sides to get 1 + r ≈ 1.0500, which means r ≈ 0.0500 or 5% when expressed as a percentage.
Hence, the rate of interest is 5% per annum (p.a.), meaning the correct answer is (A) 5 p.c.p.a.