Definition of Retirement
In general terms, retirement means a series of payments, whether made by you or coming to you. These payments:
- Have a fixed value
- Occur according to a regular schedule, such as monthly, quarterly, or annually
- Are made for a specified period, such as five years or ten years
When people talk about retirement, they often refer to an investment product offered by insurance companies. These investment tools include fixed payments contributed to retirement for a certain number of years, capital accumulation at a predetermined interest rate, and then, after retirement, fixed amounts are disbursed as substitute income.
Paying a fixed rent every month is another example of retirement where a series of regular payments is made to a property owner.
Present Value Formula
When you calculate the present value (PV) of retirement, you will be able to know the value of all the expected future retirement income.
The calculation takes into account the interest amount that the retirement pays, your monthly payment amount, and the number of periods, usually in months, that you expect to pay into retirement.
The PV calculation represents the concept of the time value of money, which states that a dollar now is worth more than a dollar earned in the future, due to the interest you can earn by investing those future dollars today.
The PV calculation uses the number of payment periods to apply a discount to future payments. You can use the following formula to calculate the present value of retirement:
PV of Retirement = P * [1 – ((1 + r)^(-n)) / r]
Where:
- P = periodic payment
- r = periodic interest rate
- n = number of periods
Please note that this equation assumes that both the payment and the interest rate remain constant throughout the retirement payment period.
Example
Let’s say you want to calculate the present value of an ordinary annuity with an annual payment of $100 and an interest rate of five percent, with the assumption that you will receive the money at the end of three years.
Using the present value formula for retirement, you can calculate the amount as follows:
Present value of retirement = $100 * [1 – ((1 + 0.05)^(-3)) / 0.05] = $272.32
When calculating the present value of retirement, remember that you are discounting the value of retirement. Discounting cash flows, such as retirement payments of $100 annually, takes into account risks over time, inflation, and the inability to earn interest on money you do not have yet. Since an annual retirement payment of $100, or $300, is not available to you today, you cannot earn interest on it, giving it a reduced value today of $272.32.
Using the formula above to solve present value problems takes a bit of time. You can use a financial calculator or a spreadsheet application to calculate present values more efficiently.
Using a Financial Calculator
You can find the present value of an ordinary annuity using any calculator that has a time value of money function, even regular (non-financial) calculators.
Financial calculators make things easier because they have individual buttons corresponding to the variables in the time value of money equations. The formula for the present value of retirement uses four of those variables. On a financial calculator, you would use the following keys and inputs:
- Press N and 3 (for three years).
- Press i or I/YR and 5 (for the interest rate of 5 percent).
- Press PMT and -100 (make sure to input it as negative 100).
- Press PV and you will reach your answer of $272.32.
Spreadsheet Calculations for Present Value
Spreadsheets like Microsoft Excel work well for calculating time value of money problems and other mathematical equations. You can either write the formula yourself or use a built-in financial function that guides you through the formula inputs.
Using the same inputs mentioned above, you can use the following formula for the present value of an ordinary annuity in your Excel spreadsheet, ensuring to enter the payment of $100 as a negative number:
=PV(rate,nper,pmt)
=PV(.05,3,-100)
To find
Instead of writing the formula, go to an Excel worksheet and click on Financial Function in the Formulas menu. Display the dropdown list and click on PV. You will see a dialog window open with spaces to fill in the information for calculating the present value.
Using the previous entries, fill in the interest rate 0.05, the time period 3 (years), and the payments -100. You will get the above function. If the formula does not calculate automatically, go to the right side of the worksheet at the top and click on Calculate to get the answer 272.32 dollars.
You can also use this online calculator to double-check your present value calculations for a regular annuity.
What about the future value?
You may consider purchasing an annuity product and want to know your retirement value at some point in the future based on what you can afford in monthly payments.
If you know how much you will pay each month, the interest rate you will receive, and the number of months or years you intend to pay into retirement, you can use a very similar formula to the present value to calculate the future value of the annuity (FV).
Use the following formula to calculate the future value of the annuity:
FV of annuity = P * [((1 + r)^(n)) – 1 / r ]
Where:
- P = periodic payment
- r = periodic interest rate
- n = number of periods
As with the present value equation, please note that the future value equation assumes that the payment and interest rate remain constant throughout the annuity payment period.
You can also use the future value formula to calculate another type of annuity, such as a loan, where you know your fixed payments, the imposed interest rate, and the number of payments. This will reveal your total cost of the loan.
The process of calculating future value using a calculator or spreadsheet works in the same way as calculating present value, except for using the future value formula and the appropriate entries to get the result.
Source: https://www.thebalancemoney.com/how-to-calculate-present-value-of-ordinary-annuity-393390
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