Solution:

Given:
Monthly Investment = Rs. 2000
Interest Rate = 6% per annum, compounded monthly
Number of Payments = 10

To find:
Future Value of the annuity after the 10th payment

Formula used:
Future Value of Annuity = PMT x (((1 + r)n - 1) / r)
Where,
PMT = Monthly Investment
r = Interest Rate / 12 (Monthly rate)
n = Number of Payments

Calculation:
PMT = Rs. 2000
r = 6% / 12 = 0.5%
n = 10

Using the formula, we get:

Future Value of Annuity = Rs. 2000 x (((1 + 0.5%)^10 - 1) / 0.5%)
= Rs. 23,629.49

Therefore, the future value of the annuity after the 10th payment is Rs. 23,629.49.

Explanation:

The given problem is an example of an annuity, where a fixed amount is invested at regular intervals for a specific period of time. In this case, Rs. 2000 is invested at the end of each month for 10 months.

To calculate the future value of this annuity, we need to use the formula of the future value of annuity, which takes into account the monthly investment, interest rate, and the number of payments.

The formula uses the power of compounding to calculate the future value of the annuity. In this case, the interest is compounded monthly, which means the interest is added to the principal amount at the end of each month, and the interest for the next month is calculated on the new amount.

Using the formula, we get the future value of the annuity after the 10th payment as Rs. 23,629.49, which means the total value of the investment after 10 months will be Rs. 23,629.49.

A=Rs. 200
n=10
i=6% p.a. =6/12% per month =0.005
Future value of annuity after 10 months is given by
A(n, i)=A[
i
(1+i)
n
−1
​
]
A(10,0.005)=200[
0.005
(1+0.005)
10
−1
​
]
=Rs. 2,044.