The formulas used in the calculations are:
\[ PV_{ga} = \frac{P}{r - g} \times \left(1 - \left(\frac{1 + g}{1 + r}\right)^n \right) \]
\[ FV_{ga} = \frac{P \times ((1 + r)^n - (1 + g)^n)}{r - g} \]
If \(r = g\):
\[ FV_{ga} = P \times n \times \frac{(1 + r)^n - 1}{r} \]
This calculator computes the present value and future value of a growing annuity based on the input values of initial payment, interest rate, growth rate, and number of periods.
Let's assume the following:
Calculate the present value of growing annuity:
\[ PV_{ga} = \frac{1,000}{0.05 - 0.03} \times \left(1 - \left(\frac{1 + 0.03}{1 + 0.05}\right)^{10} \right) \approx 8,752.97 \]
Calculate the future value of growing annuity:
\[ FV_{ga} = \frac{1,000 \times ((1 + 0.05)^{10} - (1 + 0.03)^{10})}{0.05 - 0.03} \approx 13,439.16 \]
Therefore, the present value of the growing annuity is approximately $8,752.97 and the future value is approximately $13,439.16.