Annuity Formula Calculator
Calculation Results:
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An annuity is a series of equal payments made at regular intervals. These payments can be made to you (like a pension or structured settlement) or by you (like mortgage payments or regular savings contributions). Understanding annuities is crucial for financial planning, investment analysis, and retirement calculations.
Key Concepts of Annuities
- Regular Payment Amount (PMT): This is the fixed amount of money paid or received in each period.
- Periodic Interest Rate (r): This is the interest rate applied per period. It's important to ensure this rate matches the payment frequency (e.g., if payments are monthly, use a monthly interest rate).
- Number of Periods (n): This represents the total count of payment intervals over the life of the annuity.
- Payment Timing: This distinguishes between two main types of annuities:
- Ordinary Annuity: Payments are made at the end of each period. This is the most common type, often seen in loan repayments or bond interest payments.
- Annuity Due: Payments are made at the beginning of each period. Examples include rent payments or insurance premiums. Annuities due typically accumulate more interest because each payment earns interest for one additional period.
Present Value vs. Future Value
The annuity calculator above helps you determine two critical values:
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Future Value of Annuity (FV): This is the total value of a series of payments at a specific point in the future, assuming a certain interest rate. It tells you how much your regular contributions will grow to over time. For example, if you save $100 every month for 10 years at a 5% annual interest rate, the future value would be the total amount you'd have at the end of 10 years.
The formula for the Future Value of an Ordinary Annuity is:FV = PMT × [((1 + r)n - 1) / r]For an Annuity Due, it's:FV = PMT × [((1 + r)n - 1) / r] × (1 + r) -
Present Value of Annuity (PV): This 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 future stream of income is worth today. For instance, if you are promised $100 every month for the next 10 years, the present value would be the lump sum amount you'd need today to generate those future payments.
The formula for the Present Value of an Ordinary Annuity is:PV = PMT × [(1 - (1 + r)-n) / r]For an Annuity Due, it's:PV = PMT × [(1 - (1 + r)-n) / r] × (1 + r)
How to Use the Calculator
- Enter Regular Payment Amount: Input the fixed amount of each payment.
- Enter Periodic Interest Rate (%): Input the interest rate per period as a percentage. For example, if the annual rate is 6% and payments are monthly, the periodic rate would be 0.5%.
- Enter Number of Periods: Input the total number of payment periods. If payments are monthly for 5 years, the number of periods would be 60.
- Select Payment Timing: Choose whether payments are made at the 'End of Period' (Ordinary Annuity) or 'Beginning of Period' (Annuity Due).
- Click 'Calculate Annuity': The calculator will instantly display both the Future Value and Present Value of your annuity.
Examples
Example 1: Future Value of an Ordinary Annuity (Savings)
You decide to save $200 at the end of each month for 5 years. Your savings account offers an annual interest rate of 3%, compounded monthly.
- Regular Payment Amount: $200
- Periodic Interest Rate: 3% annual / 12 months = 0.25% per month (0.0025 as a decimal)
- Number of Periods: 5 years * 12 months/year = 60 periods
- Payment Timing: End of Period
Using the calculator, the Future Value of Annuity would be approximately $12,927.30. This is how much you would have saved after 5 years.
Example 2: Present Value of an Annuity Due (Rental Income)
You own a property that generates $1,500 in rent at the beginning of each month for the next 3 years. If you could invest money at an annual rate of 4%, compounded monthly, what is the present value of this future rental income stream?
- Regular Payment Amount: $1,500
- Periodic Interest Rate: 4% annual / 12 months = 0.3333% per month (0.003333 as a decimal)
- Number of Periods: 3 years * 12 months/year = 36 periods
- Payment Timing: Beginning of Period
Using the calculator, the Present Value of Annuity would be approximately $51,990.75. This is what that future stream of rental income is worth to you today.