Solution:

Given,
Principal amount (P) = Rs. 2000
Time period (n) = 2 years
Interest rate (r) = 6% per annum
Compounding period (m) = 12 months (monthly compounding)

To find:
The equal payments at the end of each month for 2 years.

Formula to calculate the equal payments of an annuity:

EMI = P × r × (1 + r)^(n×m) / [(1 + r)^(n×m) - 1]

Where,
EMI = Equal Monthly Installment
P = Principal amount
r = Interest rate per month
n = Time period in years
m = Compounding period in a year

Calculation:

As we have to find the equal payments that are to be made at the end of each month, we need to convert the time period and interest rate into months.

n = 2 years = 24 months
r = 6% per annum = 0.5% per month

Substituting the given values in the formula to calculate EMI:

EMI = 2000 × 0.5% × (1 + 0.5%)^(24) / [(1 + 0.5%)^(24) - 1]
EMI = Rs. 94.72 (approx)

Therefore, each payment that needs to be made at the end of each month for 2 years is Rs. 94.72.

Explanation:
An annuity is a series of equal payments made at regular intervals for a fixed period of time. In this case, the annuity consists of equal payments made at the end of each month for 2 years.

To calculate the equal payments, we use the formula for the EMI of an annuity. The principal amount, time period, and interest rate are substituted in the formula to get the value of the EMI.

The interest rate is given as 6% per annum, which is converted into a monthly rate of 0.5%. The time period is given in years, which is converted into months. The principal amount is given as Rs. 2000.

Substituting the values in the formula, we get the value of the EMI as Rs. 94.72 (approx). Therefore, each payment that needs to be made at the end of each month for 2 years is Rs. 94.72.

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