The present value of an annuity is the current value of future payments from an annuity, given a specified rate of return, or discount rate. The higher the discount rate, the lower the present value of the annuity.

Because of the time value of money, money received today is worth more than the same amount of money in the future because it can be invested in the meantime. By the same logic, $5,000 received today is worth more than the same amount spread over five annual instalments of $1,000 each.

The present value of annuity formula is calculated by determining present value which is calculated by annuity payments over the time period divided by one plus discount rate and the present value of the annuity is determined by multiplying equated monthly payments by one minus present value divided by discounting rate.

The Periodic Payment amount is the expected amount to be paid by an annuity annually until it matures at its maturity date. Should a present value annuity make payments more often than annually, the value for periodic payments must be adjusted to reflect the new payment amount. For example, a semi-annual future value annuity makes 2 payments per year and the payment amount should be divided by 2.

The rate of return, also known as the discount rate, is the expected rate of return of a present value annuity that adjusts for interest, inflation, and other factors. If a present value annuity makes payments that differ from an annual basis, the value for rate of return must be adjusted. For example, a present value annuity making semi-annual payments should be divided by 2 to reflect the compounding effects of the semi-annual interest value.

Time to Maturity reflect the life of the present value annuity, generally a number of years that the present value annuity must be held until it reaches maturity. This number must be adjusted for present value annuities that make payments that differ from an annual basis. For example, a present value annuity that has a maturity time of 5 years but is semi-annual in nature would have 10 periods until maturity as 2 payments a year for 5 years, 2 times 5, results in 10 periods until maturity.

The Present Value of an Annuity is the value of a future payment in today’s dollar value. This value allows investors to compare returns of an investment with other investment opportunities or projects in order to make investment decisions.

The Present Value Annuity formula will determine at a given period, the present value of several future timely interval payments. The PV of annuity formula can be seen from the formula that it depends upon the time value of money concept, in which one-dollar amount of money in the current day is more worthy than the same dollar that shall be due at a date which is going to happen in future. Also, the PV of annuity formula takes care of the frequency of payment whether it’s annual, semi-annual, monthly, etc. and accordingly does calculations for compounding.

For example, assume you are considering investing in an annuity that makes payments of $1,000 every year for 5 years, and maintain a required rate of return of 10%. In order to work out the present value of the annuity to you today, the following calculation can be done:

PV = C * (1-1/(1+r)^{t}) / r

PV = 1,000 * (1-1/(1+0.1)^{5}) / 0.1

PV = $3,790.79

Working out the Present Value of an Annuity with the formula provided, the annuity has a value of $3,790.79 to you, the investor. Should the selling value exceed the amount calculated in the PV Annuity calculation, you would consider the annuity overvalued and may have doubts about investing. However, should the market value of the annuity be lower than the value you have calculated, you would consider the investment undervalued and may just snatch it up.

The formula is quite important not only in calculating the retirement options but this can also be used for cash outflows in case of capital budgeting, where there could be an example of rent or periodic interest paid which are mostly static hence those can be discounted back by using this annuity formula. Also, one has to be cautious while using the formula as one needs to determine if the payments are made at the beginning of the period or at the end of the period as the same can affect the values of cash flows due to compounding effects.

The present value of an annuity refers to how much money would be needed today to fund a series of future annuity payments. Because of the time value of money, a sum of money received today is worth more than the same sum at a future date. You can use a present value calculation to determine whether you'll receive more money by taking a lump sum now or an annuity spread out over a number of years.

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- See Also:
- FV Annuity,
- Perpetuities,
- PV & FV,