Calculation of Future Value of Annuity:

To calculate the future value of an annuity, we need to use the formula:

FV = PMT x (((1 + r)^n - 1) / r)

where,

FV = Future Value
PMT = Payment made at the end of each period
r = Interest rate per period
n = Number of periods

Calculation of Interest Rate per Period:

Since the interest rate is compounded monthly, we need to convert the annual interest rate to a monthly interest rate. We can do this by dividing the annual interest rate by 12.

So, the monthly interest rate = 6% / 12 = 0.5%

Calculation of Number of Periods:

Since the investment is made at the end of each month, we can calculate the number of periods by multiplying the number of years by 12.

So, the number of periods = 10 x 12 = 120

Calculation of Future Value:

Now, we can apply the formula to calculate the future value of the annuity:

FV = Rs.2000 x (((1 + 0.5%)^120 - 1) / 0.5%)
= Rs.2000 x (1.005^120 - 1) / 0.005
= Rs.2000 x 172.248
= Rs.3,44,496

Therefore, the future value of the annuity after the 10th payment is Rs.3,44,496.

Explanation:

The future value of an annuity is the total value of all the payments made at the end of each period, plus the compounded interest earned on those payments. In this case, we are investing Rs.2000 at the end of each month for 10 years, at an interest rate of 6% per annum compounded monthly.

We first calculated the interest rate per period by dividing the annual interest rate by 12. We then calculated the number of periods by multiplying the number of years by 12. Finally, we applied the formula to calculate the future value of the annuity.

The future value of the annuity tells us how much the investment will be worth in the future, assuming that the interest rate and the payment amount remain constant. This can be useful for planning and budgeting purposes.

20456.05