Mathematics · Financial Mathematics - Perpetuities and Annuities

Consider the following statements regarding annuities and perpetuities in financial modeling: Statement I: A growing perpetuity is a stream of cash flows that increases at a constant rate (g) forever, and its present value is calculated by dividing the first period's cash flow by (r - g), where r is the discount rate. Statement II: If the interest rate (r) is equal to the growth rate (g) in a growing annuity formula, the denominator becomes zero, rendering the standard formula unusable. Statement III: The present value of a perpetuity is always higher than the present value of a finite annuity with the same initial payment and interest rate. Which of the statements given above are correct?