For a certain principal invested at compound interest, the amount at the end of the 2nd year is Rs 1,800 and the amount at the end of the 3rd year is Rs 1,926. What is the annual rate of interest (per annum)?

Introduction:
This compound interest problem gives the amount at the end of the 2nd and 3rd year and asks for the interest rate. Such questions test your understanding that successive compound interest amounts are related by a constant multiplication factor of (1 + r) each year.

Given Data / Assumptions:

• Amount at the end of year 2, A2 = Rs 1,800
• Amount at the end of year 3, A3 = Rs 1,926
• Interest is compounded annually at a constant rate r
• We need to find the annual rate of interest r (in percent)

Concept / Approach:
In compound interest with annual compounding, the amount each year is obtained by multiplying the previous year amount by (1 + r). That is:
A3 = A2 * (1 + r)So the ratio A3 / A2 is directly equal to (1 + r). Once we know r as a decimal, we convert it to a percentage by multiplying by 100.

Step-by-Step Solution:
Step 1: Use the relation between A2 and A3.A3 = A2 * (1 + r)1,926 = 1,800 * (1 + r)Step 2: Solve for (1 + r).1 + r = 1,926 / 1,8001 + r = 1.07Step 3: Solve for r.r = 1.07 - 1 = 0.07r = 0.07 * 100% = 7%Therefore, the annual rate of interest is 7% per annum.

Verification / Alternative check:
We can verify by compounding once from year 2 to year 3 using 7% interest:
A3 = 1,800 * (1 + 0.07) = 1,800 * 1.07 = Rs 1,926This exactly matches the given amount at the end of the 3rd year, so the calculated rate is correct.

Why Other Options Are Wrong:

• 7.5%, 6.5%, 6%, 8%: If you use any of these rates, the factor A3 / A2 will not equal the given ratio 1,926 / 1,800. Thus, they do not satisfy the relation between the 2nd and 3rd year amounts.

Common Pitfalls:
Learners sometimes try to go back to the principal and use full formulas unnecessarily. The key observation is that consecutive compound amounts have a simple multiplicative relationship. Another pitfall is rounding too early; here the ratio 1,926 / 1,800 is exactly 1.07, making the calculation very simple.

Final Answer:
The annual rate of compound interest is 7% per annum.