Annuity Calculator

Annuities are a cornerstone of financial planning, offering predictable income streams for individuals and families. Whether you're saving for retirement, investing, or planning payments, understanding how annuities work is crucial. Our Annuity Calculator simplifies the process, helping you estimate present value, future value, interest, and total payments based on your financial goals.

• What is an Annuity?
• Formulas for Annuities
• How to Calculate Annuities

What is an Annuity?

An annuity is a series of regular payments made or received over time. These payments can be monthly, quarterly, annually, or any other frequency. Annuities are commonly used for retirement income, loan repayments, and investment returns.

Types of Annuities:

• Ordinary Annuity: Payments occur at the end of each period (e.g., rent or loan repayments).
• Annuity Due: Payments occur at the beginning of each period (e.g., lease payments).
• Payment-Based Annuity: Regular payments over time.
• Lump-Sum Annuity: A one-time payment invested or received with interest over a period.

Formulas for Annuities

Present Value (PV) of an Annuity:

For an ordinary annuity:

PV = PMT \times \dfrac{1 - (1+r)^{-n}}{r}

For an annuity due:

PV = PMT \times \dfrac{1 - (1+r)^{-n}}{r} \times (1+r)

Future Value (FV) of an Annuity:

For an ordinary annuity:

FV = PMT \times \dfrac{(1+r)^{n} - 1}{r}

For an annuity due:

FV = PMT \times \dfrac{(1+r)^{n} - 1}{r} \times (1+r)

Where:

• PMT = Payment amount per period
• r = Interest rate per period (annual rate divided by compounding frequency)
• n = Total number of payments

How to Calculate Annuities

Step-by-Step Process:

• Determine the annuity type: Is it based on regular payments or a lump sum? Does payment occur at the beginning or end of periods?
• Gather required inputs:
  • Payment amount (PMT) or Lump Sum
  • Interest rate (r)
  • Number of periods (n)
  • Compounding frequency
• Use formulas or a calculator to compute:
  • Present Value
  • Future Value
  • Total Interest
  • Total Payments

How to Use the Annuity Calculator

Our calculator is designed for simplicity and accuracy. Follow these steps:

• Choose Annuity Type: Select Payment-Based or Lump Sum-Based.
• Input Values: Enter values for Payment (PMT) or Lump Sum, Interest Rate (r), Number of Periods (n), and Inflation Rate (if applicable).
• Select Compounding Frequency: Options include annually, semi-annually, quarterly, monthly, or daily.
• Select Annuity Timing: Choose between Ordinary Annuity or Annuity Due.
• Click Calculate:
Review results for Present Value, Future Value, Total Payments, Total Interest, and Real Present Value (adjusted for inflation).

Examples

Example 1: Ordinary Annuity

You invest $500 monthly at a 5% annual interest rate compounded monthly for 10 years.

Inputs:

• PMT = 500
• r = 5%/12 = 0.004167
• n = 10 * 12 = 120

Results:

• PV = $47,170.96
• FV = $77,917.31
• Total Interest: FV−TotalPayments = $17,917.31

Example 2: Lump Sum Annuity

You invest $10,000 as a lump sum at a 3% annual interest rate compounded quarterly for 5 years.

Inputs:

• Lump Sum: PV = 10,000
• r = 3%/4 = 0.0075
• n = 5 * 4 = 20

Results:

• FV = $11,616.18