Present/future value of an annuity

This annuity calculator can determine both the present and future values of an annuity. By default, it calculates these values based on a $75periodic deposit (Pmt) with a periodic interest rate (I/Y) of 6% over 15 periods (N). To calculate a different present or future value, you can modify at least one of the following fields: Periodic Deposit, Interest Rate (%), or Number of Periods. As you make changes, the calculator will automatically update the future value, chart, and schedule fields.

To do the calculations for growing annuities, simply increase the Growth Rate (g).

By default, the calculator works with ordinary annuities. If you want to calculate values for an annuity due, simply select ‘Beginning of period’ below.

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What is an annuity?

An annuity is a financial product or investment that involves a series of periodic payments or receipts of a fixed amount over a predetermined period of time. Annuities are commonly used for retirement planning and income generation because they can provide a steady stream of income over a specified period, typically in the form of regular payments.

Formulas

Present value of an annuity:

The formula for calculating the present value (PV) of an annuity is:

\text{PV} =\frac{Pmt}{r} \times \left(1 - \frac{1}{(1 + r)^n}\right)

where:

• PV is the present value of the annuity (the current value of all future payments).
• Pmt is the periodic payment (the fixed amount you receive or pay at regular intervals).
• r is the interest rate per period (expressed as a decimal).
• n is the number of periods (the total number of payments or compounding periods).

P_t = P_{t-1} + \epsilon_t

Future value of an annuity:

The formula for calculating the future value (FV) of an annuity is:

\text{FV} =Pmt \times \frac{((1 + r)^n - 1)}{r}

where:

• FV is the future value of the annuity (the total amount of money accumulated or received).
• Pmt is the periodic payment (the fixed amount you receive or pay at regular intervals).
• r is the interest rate per period (expressed as a decimal).
• n is the number of periods (the total number of payments or compounding periods).

Present value of a growing annuity:

The formula for calculating the present value (PV) of a growing annuity is:

\text{PV} = \frac{Pmt}{r - g} \times \left(1 - \left(\frac{1 + g}{1 + r}\right)^n\right)

where:

• PV is the present value of the annuity (the current value of all future payments).
• Pmt is the periodic payment (the fixed amount you receive or pay at regular intervals).
• r is the interest rate per period (expressed as a decimal).
• n is the number of periods (the total number of payments or compounding periods).
• g is the growth rate of the annuity (the rate at which the payments increase over time).

Future value of a growing annuity:

The formula for calculating the future value (FV) of a growing annuity is:

\text{FV} =Pmt \times \frac{((1 + r)^n - (1+g)^n)}{r-g}

where:

• FV is the future value of the annuity (the total amount of money accumulated or received).
• Pmt is the periodic payment (the fixed amount you receive or pay at regular intervals).
• r is the interest rate per period (expressed as a decimal).
• n is the number of periods (the total number of payments or compounding periods).
• g is the growth rate of the annuity (the rate at which the payments increase over time).

Present value of an annuity due:

The formula for calculating the present value (PV) of an annuity due is:

\text{PV} =\frac{Pmt}{r} \times \left(1 - \frac{1}{(1 + r)^n}\right) \times (1+r)

where:

• PV is the present value of the annuity (the current value of all future payments).
• Pmt is the periodic payment (the fixed amount you receive or pay at regular intervals).
• r is the interest rate per period (expressed as a decimal).
• n is the number of periods (the total number of payments or compounding periods).

Future value of an annuity due:

The formula for calculating the future value (FV) of an annuity due is:

\text{FV} =Pmt \times \frac{((1 + r)^n - 1)}{r} \times (1+r)

where:

• FV is the future value of the annuity (the total amount of money accumulated or received).
• Pmt is the periodic payment (the fixed amount you receive or pay at regular intervals).
• r is the interest rate per period (expressed as a decimal).
• n is the number of periods (the total number of payments or compounding periods).

Present value of a growing annuity due:

The formula for calculating the present value (PV) of a growing annuity due is:

\text{PV} = \frac{Pmt}{r - g} \times \left(1 - \left(\frac{1 + g}{1 + r}\right)^n\right) \times (1+r)

where:

• PV is the present value of the annuity (the current value of all future payments).
• Pmt is the periodic payment (the fixed amount you receive or pay at regular intervals).
• r is the interest rate per period (expressed as a decimal).
• n is the number of periods (the total number of payments or compounding periods).
• g is the growth rate of the annuity (the rate at which the payments increase over time).

Future value of a growing annuity due:

The formula for calculating the future value (FV) of a growing annuity due is:

\text{FV} =Pmt \times \frac{((1 + r)^n - (1+g)^n)}{r-g} \times (1+r)

where:

• FV is the future value of the annuity (the total amount of money accumulated or received).
• Pmt is the periodic payment (the fixed amount you receive or pay at regular intervals).
• r is the interest rate per period (expressed as a decimal).
• n is the number of periods (the total number of payments or compounding periods).
• g is the growth rate of the annuity (the rate at which the payments increase over time).

Annuity types

There are several types of annuities, and they can be classified based on the timing of the payments and the direction of cash flows:

1. Fixed annuity: In a fixed annuity, the annuitant (the person who owns the annuity) makes regular payments to the insurance company, and in return, the insurance company guarantees a fixed interest rate for the duration of the contract. The periodic payments to the annuitant are usually fixed and do not vary.
2. Variable annuity: With a variable annuity, the annuitant’s payments are invested in a variety of sub-accounts, similar to mutual funds. The return on investment is not guaranteed and can fluctuate based on the performance of the chosen investments. Variable annuities offer the potential for higher returns but come with more risk.
3. Immediate annuity: In an immediate annuity, the annuitant makes a lump-sum payment to the insurance company and starts receiving periodic payments immediately, typically within one year of the initial investment. Immediate annuities are often used to provide a guaranteed stream of income in retirement.
4. Deferred annuity: A deferred annuity involves making payments to the insurance company over a period of time, and the annuitant starts receiving payments at a future date, typically in retirement. Deferred annuities can be fixed or variable and are used for long-term retirement planning.
5. Annuity due: An annuity due is similar to a regular annuity, but the payments are made at the beginning of each period, rather than the end. This means that the first payment is received immediately.
6. Perpetuity: A perpetuity is a type of annuity that lasts indefinitely, with periodic payments that continue forever. The formula for the future value of a perpetuity simplifies to (FV = Pmt/r), where (Pmt) is the periodic payment, and (r) is the interest rate.

Examples of annuities include:

• A retiree receiving monthly pension payments.
• An individual purchasing a fixed immediate annuity to provide a guaranteed monthly income in retirement.
• An investor contributing to a 401(k) retirement account, which is a form of a deferred annuity.
• An insurance policy that provides periodic payments to beneficiaries after the death of the policyholder (a form of life insurance annuity).
• An individual contributing to a variable annuity contract with investments tied to the stock market.

The choice of annuity type depends on individual financial goals, risk tolerance, and the need for a guaranteed income stream. It’s essential to carefully consider the terms and conditions of any annuity contract before investing.