According to the given information, we need to calculate the present value of an annuity of 3000 for 15 years at 4.5% per annum compounded annually. To do this, we can use the formula for the present value of an ordinary annuity.

Formula:
The formula for the present value of an ordinary annuity is:
PV = P * [(1 - (1 + r)^(-n)) / r]

Where:
PV = Present Value
P = Payment or annuity amount
r = Interest rate per period
n = Number of periods

Given data:
P = 3000 (annuity amount)
r = 4.5% per annum (interest rate)
n = 15 years (number of periods)

Step 1: Convert the interest rate and number of periods:
Since the interest rate is given as an annual rate, we need to convert it to a rate per period. In this case, the interest is compounded annually, so the rate per period is the same as the annual rate. Therefore, r = 4.5% per annum.

The number of periods is already given as 15 years.

Step 2: Calculate the present value:
Using the formula for the present value of an ordinary annuity, we can substitute the given values and calculate the present value.

PV = 3000 * [(1 - (1 + 0.045)^(-15)) / 0.045]

Calculating the expression inside the brackets:

= 3000 * [(1 - (1.045)^(-15)) / 0.045]
= 3000 * [(1 - 0.508395) / 0.045]
= 3000 * (0.491605 / 0.045)
= 3000 * 10.9245556
= 32773.67 (rounded to two decimal places)

Therefore, the present value of the annuity is approximately 32773.67.

Explanation:
The present value of an annuity is the current value of a series of future cash flows discounted at a given interest rate. It represents the amount of money that would need to be invested today at the given interest rate to generate the same future cash flows.

In this case, we have an annuity of 3000 per year for 15 years, and the interest rate is 4.5% per annum compounded annually. By using the formula for the present value of an ordinary annuity, we can calculate the present value, which is approximately 32773.67.

Conclusion:
The present value of an annuity of 3000 for 15 years at 4.5% per annum compounded annually is approximately 32773.67. This means that if someone wants to receive 3000 per year for 15 years at an interest rate of 4.5% per annum, they would need to invest approximately 32773.67 today.