# How to Calculate Present Value for Retirement in 15 Yrs

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"Present value" is the amount of money that, if invested today at a constant interest rate for a period of time, will grow to a certain "future value." There are three ways to calculate present value (PV); with an equation, an interest rate table--such as one from a financial textbook--or a financial calculator.

### Things You'll Need

• Pencil and paper
• Financial calculator
• Present Value Interest Rate Table

## Calculating PV Using a Formula and/or an Interst Rate Table

• Calculate PV using this formula: PV = FV x PV [1 / (1+i)n] where "i" equals the interest rate at which your investment is expected to grow, and "n" is the number of periods for which the investments will grow ("n" is an exponent in the above equation). To calculate the PV of a retirement account in 15 years, where interest is paid annually, "n" is equal to 15.

• If you wish for the future value of your retirement account to be \$4,000,000 in 15 years and you expect to earn a 10% return on your investment each year for the next 15 years, the equation will read:
PV = 4000000 x PV [1 / (1+i)n]. Please note that in this equation, the "n" is an exponent.

• Another tool is a factor table, which can be found in a financial text book, such as "Foundations of Financial Management", which can be purchased online. For 15 periods at 10% interest, the PV factor found is 0.239. The above formula restated is:
PV = FV X PVif . To calculate the PV of a \$4,000,000 retirement account in 15 years, solve the following: PV = 4000000 x 0.239. "PVif" stands for the "present value interest factor", which is found on an interest rate table (See Resources 1). Download a PV interest factor table for free.

## Calculating PV Using a Financial Calculator

• If you have a financial calculator, you will see buttons on the calculator labeled: "N", "I/Y", "PV", "PMT", "FV".

If you have a graphing calculator with financial applications, view the "APPS" menu. Select "Finance". In the next menu, select "TVM Solver". The next screen should display the following:
N
I%
PV
PMT
FV
P/Y
C/Y
PMT: END BEGIN

• On a graphing calculator, enter the following inputs to the right of each character:
N = 15
I% = 10
PV = 0
PMT = 0
FV = 4000000
P/Y = 1
C/Y = 1
PMT: "END" should be highlighted; if not, use navigation arrows to highlight "END"

On a financial calculator, use the same inputs. You will enter the value, such as "10" for the interest rate; press the "I/Y" button for interest after entering the value.

• On the financial calculator: after entering all values, press "CPT" (short for compute), immediately followed by the "PV" button.

On the graphing calculator: after entering all values, place the cursor over the zero to the right of
"PMT =". Press the "Alpha" button, located on the top left side of your calculator, and immediately press the "Enter" button. The "Enter" button acts as a "Solve" button when pressed immediately after the "Alpha" button. "Solve" should be printed above the "Enter" button in a color text that matches the color of the "Alpha" button.

On the graphing calculator: your screen should read "-957,568.2" next to "PV".

## Tips & Warnings

• The number of periods is dependent upon how frequently interest is earned. For example, if interest is paid semiannually, then "n" would be equal to 30, based on a 15-year projection.
• When speaking of PV, the interest rate is actually called a "discount rate".
• To download the Time Value of Money Present Value Factor table:
• Visit the resource site: www.tvmcalc.com.
• Select the "Calculators" tab.
• Scroll past the beginning paragraphs of "Create Time Value of Money Tables in Excel".
• Find at the the bottom of this section, an excel download link: "You can download a complete copy of the 'Time Value of Money Interest Factors workbook'".
• Notice that the answer is different when calculated using a table vs. using the calculator. This is because the interest rate factor from the table is rounded, while a calculator can include additional tenths and thousandths, which is additional money that compounds over time at the interest rate.

## References

• Photo Credit Comstock/Comstock/Getty Images
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