Present Value Calculator

More about the this present value calculator so you can better understand how to use this solver

The present value (\(PV\)) of a certain amount of money that will have certain future value (\(FV\)) after a number of years, depends on the number of years \(n\) when the money will be received, the interest rate \(r\), the type of compounding (yearly, bi-yearly, quarterly, monthly, weekly, daily or continuously). Let \(k\) be the number of times the money is compounded in a year. For example, for yearly compounding we have \(k = 1\), for bi-yearly compounding we have \(k = 2\), for quarterly compounding we have \(k = 4\), etc.

How do you calculate present value?

The present value (\(PV\)) can be computed using the following formula:

\[ PV = \frac{FV}{\left( 1+\frac{r}{k}\right)^{ k \times n} } \]

For continuous compounding, we get that \(k \to \infty\), in which case we need to use the following compounded formula instead.

\[ PV = \frac{FV}{e^{r \times n}} \]

What this present value calculator does is simply find a compounding factor, which is used to bring future money into present money. The same task can be conducted with Excel, using the PV() function, with the difference that this calculator shows all the steps.

Present value calculator with payments

Notice that this calculator does not include the possibility of payments. If there are periodic payments, then you should use an annuity calculator , and the more general case of computing the net present value of a sequence of flows, you can use this net present value calculator .

Future value calculator

What is the difference between a present value calculator and a future value calculator? It is usually easier to think about it in terms of money in the bank.

Indeed, the present value is how much you would need to put in the the bank TODAY, if you wanted to reach certain specific objective in a number of years. On the other hand, the future value can be understood as how much you will have in the future, if you put in the bank a certain amount today.

So then, if instead you know the present value and you want to compute the future value, use this step-by-step calculator .

How do you calculate net present value, is it related to the present value?

The concepts of present value and net present value are tightly related. Present value of a cash flow is the value in today's money of a future cash flow. On the other hand, the net present value calculation consists of the calculation and sum of present values of ALL future cash flows associated to a project.

Example of PV calculation

Question: How much money do you need to put in the bank today if you want to get $40,000 after 20 years, if the bank gives you 4% annually, compounded bi-yearly?

Solution:

This is the information we have been provided with:

• The future value is \(FV = 40000\), the yearly interest rate is \(r = 0.04\). The total number of years is \(n = 20\), and the compounding is done biyearly.

Hence, the present value for the given future value after 20 periods is calculated using the following formula:

\[ \begin{array}{ccl} PV & = & \displaystyle \frac{FV}{\left( 1+\frac{r}{k}\right)^{ k \times n}} \\\\ \\\\ & = & \displaystyle \frac{ 40000}{\left( 1+\frac{ 0.04}{ 2}\right)^{ 2 \times 20}} \\\\ \\\\ & = &\displaystyle \frac{ 40000}{\left( 1+ 0.02 \right)^{ 2 \cdot 20}} = \frac{40000}{ 2.208} \\\\ \\\\ & = & 18115.6166 \end{array} \]

which means that the present value for a future value of \(FV = 40000\), for a yearly interest rate of \(r = 0.04\), \(n = 20\) years, and with biyearly compounding is \( PV = \text{\textdollar}18115.62 \).