To find the future value of an annuity where regular payments are made into an account that earns interest compounded periodically, we use the future value of an ordinary annuity formula:

$FV = P \times \frac{(1 + r)^n - 1}{r}$

where:

• $FV$ is the future value of the annuity,
• $P$ is the payment amount,
• $r$ is the interest rate per period,
• $n$ is the number of payments.

Given:

• Monthly payment ($P$) = ₹200
• Annual interest rate = 6% per year
• Monthly interest rate ($r$) = $\frac{6\%}{12}$ = $\frac{0.06}{12}$ = 0.005
• Number of payments ($n$) = 10
• $(1.005)^{10} = 1.0511$ (Given)

Now, substitute the values into the formula:

$FV = 200 \times \frac{1.0511 - 1}{0.005}$

$FV = 200 \times \frac{0.0511}{0.005}$

$FV = 200 \times 10.22$

$FV = ₹2044$

So, the future value of the annuity after the 10th payment is ₹2044.

Would you like more details or have any questions?

Here are some related questions:

1. How would the future value change if the interest rate was compounded quarterly instead of monthly?
2. What is the impact on future value if the number of payments increases?
3. How does the future value differ for different payment intervals, like annual or weekly?
4. What is the present value of this annuity, given the same interest rate and payment structure?
5. How does the future value formula change if payments are made at the beginning of each period?

Tip: When dealing with annuities, be mindful of whether payments are made at the beginning or end of each period; this distinction affects the future value calculation.