SPONSORED

Present Value (PV) Calculator

LAST UPDATE: September 29th, 2018

Present Value Calculator

What is Present Value (PV)?

Present Value (PV) is the current value of future money.

It is today’s value of a future lump sum or future series of payments. It calculates today’s value of future money using an interest rate and number of time periods.

How is the Present Value calculated?

Present value calculates through a financial formula used to determine the time value of money.
There are two separate calculations involved: The base sum as well as the payment schedule.
For the base sum, the formula is:

\text{Present Value} = \frac{\text{Future Value}}{(1 +\text{Rate of Return})^\text{Periods}}

For a payment annuity that occurs at the end of each period (present value of an annuity), the formula is:
\text{Present Value} = \text{Payment} \times (\frac{1 - (1 + \text{Rate of Return})^(-\text{Periods)}}{\text{Rate of Return}})

For a payment annuity that occurs at the beginning of each period (present value of an annuity due), the formula is:
\text{Present Value} = \text{Payment} \times (\frac{(1 + \text{Rate of Return})^\text{Periods} - 1}{\text{Rate of Return}}) \times (1 + \text{Rate of Return})

Example

We are looking to save $2,000 over 10 years in an account that earns 2.2% interest per year. At the end of each year, we will pay $100 into the account. How much would we have to put into the account at the start of the saving period to reach the $2,000 goal?
Step 1: Calculate the present value of the fixed portion
\text{Present Value} = \frac{2,000}{(1 + 0.022)^10}
\text{Present Value} = \frac{2,000}{(1.022)^10}
\text{Present Value} = \frac{2,000}{1.243108}
\text{Present Value} = 1,608.87
Step 2: Calculate the present value of the payment annuity
\text{Present Value} = 100 \times (\frac{1 - (1 + 0.022)^-10}{0.022})
\text{Present Value} = 100 \times (\frac{1 - (1.022)^-10}{0.022})
\text{Present Value} = 100 \times (\frac{1 - 0.804435}{0.022})
\text{Present Value} = 100 \times (\frac{0.195565}{0.022})
\text{Present Value} = 100 \times 8.889318
\text{Present Value} = 888.93
Step 3: Add the two together
\text{Present Value} = 1,608.87 + 888.93
\text{Present Value} = 2,497.80
The present value of the account would be 2,497.80.

What is Future Value?

Future Value (FV) is the total value at the end of the time period.

What are periods?

Periods are the number of times that compounding (and payments) take place.

What is the rate?

The rate is the amount of interest earned per compounding period.

What is Payment (PMT)?

A payment is an amount either deposited or withdrawn at each compounding period. A negative number designates an amount that is deposited, while a positive one withdrawn. For example, if $100 is deposited each compounding period, it would be entered as '-100', while if $75 was payed out each compounding period, it would be entered as '75'.

What are Payments at start or end of a period?

A payment at the beginning of a period would mean that the payment (or deposit) occurs at the beginning of each period. A payment at the end of a period would mean that the payment (or deposit) occurs at the end of each period.

Sources and External Resources

More Time Value of Money Calculators