What is the formula for a quarterly growing annuity?

The formula for a quarterly growing annuity is indeed presented correctly. This formula is used to calculate the present value of a series of cash flows that grow at a constant rate, g, over time, while being discounted at a different rate, r.

In this context, C represents the cash flow received each period, m indicates the number of compounding periods per year (for quarterly payments, m would be 4), and t represents the total number of years the annuity is expected to last.

The formula accounts for:

1. The growing nature of the cash flows: Each cash flow increases by the growth rate g.

2. The discounting effect of the rate r, reflecting the time value of money.

The term (1 - (1 + g)/(1 + r)^tm) reflects the adjustment needed to sum the present value of cash flows that increase each period, ensuring accurate valuation based on the expected growth and discount rates. This is crucial when determining the value of cash flows over multiple periods, particularly when those cash flows vary over time due to growth.

The other choices do not correctly reflect the dynamics of a growing annuity in relation to both the growth and discounting aspects, which is why they do not serve as valid