# Future Value Of Annuity Calculator

Future Value Of annuity is the amount paid in or out for each period. The annual nominal interest rate  Expressed as a percentage. Annuity term constitutes lifespan of the annuity.The interest is compounded number of time.

Let us consider,

• Payment amount (PMT) is the amount paid in or out (cash flow) for each period.
• Interest rate (r) is the annual nominal interest rate expressed as a percentage.
• Annuity term constitutes the lifespan of the annuity.
• Compounding frequency (m) refers to the number of times the interest is compounded.
• Payment frequency (q) indicates how often the payments will materialize.
• Type of annuity (T) signifies the timing of the payment in each payment period (ordinary annuity: end of each payment period; annuity due: the beginning of each payment period).
• Future value of annuity (FVA) the future value of any present value cash flows (payments).
• Growth rate of annuity (g) is the percentage increase of an annuity in the case of a growing annuity.
• Number of periods (t) shows the annuity term in years.
• Equivalent interest rate and Periodic equivalent interest rate are the interest rates computed when the payments and compounding occur at a different frequency (cannot be set manually).

annuity formula us,

• Ordinary Annuity:FVA = PMT / i * ((1 + i) ^ n – 1)
• Annuity Due:FVA = PMT / i * ((1 + i) ^ n – 1) * (1 + i)

let us consider,

n = m * t where n is the total number of compounding intervals

i = r / m where i is the periodic interest rate (rate over the compounding intervals)

• Future Value of a Growing Annuity (g ≠ i):FVA = PMT / (i – g) * ((1 + i) ^ n – (1 + g) ^ n)
• Future Value of a Growing Annuity (g = i):FVA = PMT * n * (1 + i) ^ (n – 1)
• Future Value of an Annuity with Continuous Compounding (m → ∞)

FVA = PMT / (eʳ – 1) * (eʳᵗ – 1)