# Finding the Present Value Factor of an Annuity

Finding the present value factor of an annuity involves calculating compounding interest over a given number of years based off a desired end-goal. An annuity calculator can be used to find the present value of a fixed annuity by entering an interest rate, the number of years will be compounding, and the final total you'd like to achieve. Present value calculations use the same formula as future value, but solve for a different variable. Calculating the present value is useful in a situation like retirement planning, where you have firm financial objective in mind. To calculate the present or future value of your annuity, use the free calculators below:

» Present Value Annuity Calculator

» Future Value Annuity Calculator

## Calculating Compound Interest

The formula for compound interest is as follows: FV = PV (1+i)^n  where FV stands for future value, PV stands for present value, i stands for interest, and n stands for number of years. Let's run through a basic calculation. What would a \$30,000 initial investment yield after 5 years of compounding interest at 5%? That's simple enough, we just need to solve for FV.

FV = 30,000 (1+0.05)^5 = 30,000 * 1.05 * 1.05 * 1.05 * 1.05 * 1.05 = \$38,288

Here's how we make sense of this formula: the first year our hypothetical annuity investor starts off with \$30,000. At 5% interest, at the end of year one, this premium grows to \$31,500. The second year our annuity experiences the same 5% growth, but the initial investment has grown, so to speak. At the end of year two the total balance becomes \$33,075. And so this trends continues, compounding the initial \$30,000 over and over again for 5 years.

## Present Value Annuity Calculation

A present value annuity calculator is used to determine how much one would have to invest in an annuity to get a certain total in the end. This is the reverse of a future value annuity calculation, which is used to determine how much a certain initial investment will grow over time. The formula for present value is: PV = FV / (1+i)^n. Let's run through a present value calculation: How much would we need to invest today to end up with \$500,000 in 4 years, assuming a 9% rate of return? The math goes like this:

PV = 500,000 / (1+0.09)^4 = 500,000 * 1/(1.09 * 1.09 * 1.09 * 1.09) = \$354,212

In this case our hypothetical investor would have to place \$354,00 in his annuity to end up with \$500,000 in 4 years.

## Factors of a Present Value Calculation

The mathematical formula for the discount factor is the reciprocal of 1+ the rate of return. Factors of present value calculation include the contract's term (in years), the interest rate (in %), and the final amount (in \$). These three variables determine the initial contribution you'd need to make to meet your final amount. As long as the rate of return stays constant (as with a fixed annuity or cd-type annuity) the final amount will be guaranteed.

## Present Value Annuity Example

John is planning his retirement and estimates that he'll need \$300,000 by the time he reaches the age of 65. John's currently 50 years old and has found a fixed rate annuity that guarantees 8% interest for 15 years. How much should John invest today to meet his retirement savings goal? For this we need to calculate the present value of \$300,000.

PV = 300,000 / (1+0.08)^15 = \$94,572

This future value calculation gives John a good ballpark of how much he should be investing right now. A smart decision here would be to invest part of the \$100,000 in a fixed annuity, part in a money market account, and part in an equity vehicle like a mutual fund or equity-indexed annuity. This diversification would provide added security and give John a shot at beating his \$300,000 mark.

## Retirement Planning with Present Value

Calculations for the present value of an annuity are used by financial professionals for retirement planning. First it's determined how much one would need upon retirement to live comfortably, then the initial investments one would need to make to meet that goal are calculated. Identifying your financial objectives before investing is important, especially for annuities, because you don't want to run out of savings half-way through retirement.

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