Annuity Calculator
Use this calculator to determine the future value or present value of an annuity, considering regular payments, interest rate, compounding frequency, and the duration of the annuity.
Results:
Future Value of Annuity:
Present Value of Annuity:
Understanding Annuity Calculations
An annuity is a series of equal payments made at regular intervals over a specified period. Annuities are common in financial planning, such as retirement savings, loan repayments, and insurance payouts. Understanding how to calculate the future value (FV) and present value (PV) of an annuity is crucial for making informed financial decisions.
Key Components of an Annuity
- Regular Payment Amount (P): The fixed sum of money paid or received at each interval.
- Annual Interest Rate (r): The stated annual rate at which the annuity grows or discounts.
- Compounding Frequency: How often the interest is calculated and added to the principal within a year (e.g., monthly, quarterly, annually). This affects the effective interest rate per period and the total number of periods.
- Number of Years (n): The total duration over which the annuity payments are made.
- Annuity Type:
- Ordinary Annuity: Payments are made at the end of each period. This is the most common type.
- Annuity Due: Payments are made at the beginning of each period. This means each payment earns one extra period of interest compared to an ordinary annuity.
Future Value of an Annuity (FVA)
The future value of an annuity is the total value of a series of payments at a specific point in the future, assuming a certain interest rate and compounding frequency. It tells you how much your regular contributions will be worth by the end of the annuity term.
The formula for the Future Value of an Ordinary Annuity is:
FVA = P * [((1 + r_per_period)^n_periods - 1) / r_per_period]
For an Annuity Due, the formula is:
FVA_due = FVA_ordinary * (1 + r_per_period)
Where:
P= Regular Payment Amountr_per_period= Interest rate per compounding period (Annual Rate / Compounding Frequency)n_periods= Total number of compounding periods (Number of Years * Compounding Frequency)
Present Value of an Annuity (PVA)
The present value of an annuity is the current value of a series of future payments, discounted back to the present using a specific interest rate. It tells you how much a lump sum today would be worth if it could generate the same series of future payments.
The formula for the Present Value of an Ordinary Annuity is:
PVA = P * [(1 - (1 + r_per_period)^-n_periods) / r_per_period]
For an Annuity Due, the formula is:
PVA_due = PVA_ordinary * (1 + r_per_period)
Where the variables are the same as for the future value calculation.
How to Use the Calculator
- Enter Regular Payment Amount: Input the fixed amount paid or received each period.
- Enter Annual Interest Rate (%): Provide the annual interest rate as a percentage (e.g., 5 for 5%).
- Select Compounding Frequency: Choose how often interest is compounded (e.g., monthly, annually).
- Enter Number of Years: Specify the total duration of the annuity in years.
- Select Annuity Type: Choose between Ordinary Annuity (payments at end of period) or Annuity Due (payments at beginning of period).
- Click "Calculate Annuity": The calculator will display both the Future Value and Present Value of your annuity.
Example Scenario
Imagine you contribute $500 per month to a retirement account for 20 years, and the account earns an average annual interest rate of 7%, compounded monthly. This is an ordinary annuity (payments at the end of the month).
- Regular Payment Amount (P): $500
- Annual Interest Rate: 7%
- Compounding Frequency: Monthly (12 times per year)
- Number of Years: 20
- Annuity Type: Ordinary Annuity
Using the calculator with these inputs would show you the substantial future value of your consistent contributions, as well as the present value of that future income stream.