How To Calculate the Present and Future Value of Annuity
Have you ever bought a ticket for one of those huge lottery jackpots? Five hundred million dollars! Eight hundred million dollars! One and a half billion dollars! But if you look at the fine print, you’ll see something called the “cash option,” which is how much you’d get if you opted for a lump sum instead of 30 annual payments.
What’s the difference? And how do you know which one to choose? Making this choice is a problem many people think they’d love to have, so here’s a look at what it all means.
See: 3 Things You Must Do When Your Savings Reach $50,000
Read: The Simple, Effective Way To Fortify Your Retirement Mix
Annuities and How They Work
Lottery jackpots are calculated based on an annuity, which is a series of payments that are made at regular intervals until a total is reached. If you win the lottery, these payments would be made to you each year, and at the end of 30 years, you’d have the total amount of that huge jackpot.
A series of equal payments you make to someone else is also an annuity. An example of this could be the rent you pay to your landlord.
The future value of an annuity is the total value of payments at a specific point in the future. This is the “jackpot” amount that the lotteries tout as how much you could win–if you can beat the odds.
The present value is how much money you would need now in order to generate those future payments. Think of this as the “cash option” in the lottery example.
Future Value of an Annuity
The future value of an annuity is the amount that regular payments will be worth at some point in the future at a specific interest rate. In addition to informing your decision on how to collect your lottery winnings, this calculation is useful if you’re going to invest a specific amount of money each month at a specified rate of interest (or return) and want to know how much money you’ll have after a certain amount of time. These regular payments are also considered an annuity in the broadest sense of the word.
Here’s how to calculate the future value of an annuity.
The formula is:
(FV) = A x [((1+i)n -1)/i]
Where:
FV = future value of the annuity
A = the annuity payment per period
n = the number of periods
i = the interest rate
Present Value of an Annuity
If you know what the future monthly payments would be worth now, you need to calculate the present value of the annuity. This will tell you the amount of money you would need to have to generate the monthly payments.
Here’s how to calculate the present value of an annuity.
The formula is:
(PV) = ΣA / (1+i) ^ n
Where:
PV = present value of the annuity
A = the annuity payment per period
n = the number of periods
i = the interest rate
There are online calculators that make it much easier to compute the future or present value of an annuity, but it’s important to understand the underlying concepts of each.
The Time Value of Money
Both of these calculations are based on the time value of money. The time value of money means that money that you have today is more valuable than the same amount of money in the future because you will be able to earn money on the money you have today.
If you know the present value and want to find the future value, the calculation is:
FV = PV (1 + i / n)nt
Where:
FV = future value
PV = present value
i = interest rate
n = the number of times the amount is compounding (so, 12 if it’s compounding monthly)
t = time in years
If you know the future value and want to find the present value, the calculation is:
PV = FV / (1 + (i / n)nt
PV = present value
FV = future value
i = interest rate
n = the number of times the amount is compounding (so, 12 if it’s compounding monthly)
t = time in years
Annuities Due and Ordinary Annuities
When it comes to trying to calculate the present or future value of an annuity, it’s important to understand that there are two basic types. The type of annuity depends on whether the payments come at the beginning or the end of the period. The period could be a month, a year, or some other period of time. An annuity that makes or requires payment at the beginning of each period is known as an annuity due.
An annuity that makes or requires payment at the end of each period is known as an ordinary annuity. When you win the lottery, you’ll get one payment on the spot, and the remaining payments as an ordinary annuity, so, at the end of each subsequent year.
The above examples are for ordinary annuities.
What About Other Kinds of Annuities?
The formulas for calculating the present and future value of annuities are the same regardless of the type of annuity you’re talking about. But there are some annuities that are sold as investments that promise a lifetime benefit – a monthly payment for as long as you live.
With these kinds of annuities, the investor deposits either a lump sum of money or makes periodic payments to the annuity company. The money returns either a fixed rate, in the case of a fixed annuity, or a rate that is tied to investments like mutual funds that can fluctuate, in the case of a variable annuity.
Later on, typically when the investor retires, they will begin taking a stream of income from the annuity. This means they get a payment every month that is guaranteed for the rest of their life.
These are more challenging to calculate since you don’t know how many payments you will get. These kinds of annuities are sold by insurance companies because they have the ability to predict how long someone is likely to live and to plan the payments accordingly. Using the same kind of actuarial table they use to calculate the price for life insurance, these companies estimate your life expectancy and set your annuity payments accordingly.
Investors who live longer than average may collect more money than the sum of their investment and their return, even after factoring in the future value of the annuity contract. For those who don’t live as long as expected, they will collect less. Once these kinds of annuity contracts are annuitized, meaning they begin making payments to the investor, there is typically no death benefit should the investor die prematurely.
Calculating the present or future value of an annuity may seem complicated, but it’s just a matter of having the right information and using the right formula. And if all else fails, try an online calculator.
FAQ
Here's what you should know about annuity formula and calculating present and future value.
How do you calculate an annuity?
In order to calculate the value of an annuity, you need to know the amount of each payment, the frequency of payments, the number of payments and the interest rates. To calculate the present value, use this formula: (PV) = ΣA / (1+i) ^ n. To calculate the future value, use this formula: (FV) = A x [((1+i)n -1)/i].
How much does a $100,000 annuity pay per month?
The amount of money an annuity pays per month depends on the value of the annuity, the number of months it will pay out, and the interest rate. There are annuity calculators online that can help to determine the monthly payout if you have this information.
What is the formula for return on an annuity?
To calculate the return on an annuity, take the current value and subtract the amount you invested. Divide that by the amount you invested and multiply by 100. For example, suppose you invested $100,000 in an annuity that is now worth $120,000. The current value of $120,000 minus your contribution of $100,000 is $20,000. $20,000 divided by your contribution of $100,000 is .02, times 100 is 20. Your rate of return is 20%.
This article originally appeared on GOBankingRates.com: How To Calculate the Present and Future Value of Annuity
