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?

There are different ways to calculate the present value of future flows, and it all depends on how the flows are structured and what the discount rate is.

The simplest way is possibly to rely on a finance calculator, but here we will learn how to use the present value formula, which provides you with the advantage of getting a stronger understanding of what is actually going on with the calculation process.

The present value formula

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

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

See that the above formula uses different values of \(k\), which represent different types of compounding. A commonly used one is \(k=1\) for yearly compounding, but you can choose whichever you prefer.

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

How do you calculate PV with PMT?

The formula that we have been showing until now assumes that there is only one future flow, which is discounted in order to convert it into a present flow.

A situation that occurs in reality very often that there are also recurrent payments that need to be accounted, in which case there is one more future flow to deal with.

One such example would be one of a mortgage payment, which consists of recurrent payments made in order to pay off a mortgage loan. For that, you can use this mortgage payment calculator with steps, that also includes a complete amortization table.

Present value calculator with payments

As we noticed above, this calculator does not include the possibility of payments. If there are periodic payments that you need to take into account, 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 .

How do you manually calculate PV?

The one way to manually compute PV is to use a suitable formula, in which you take into account all future flows and discount them accordingly.

The structure of payments, in terms of how much they are an when the occur can greatly vary, so often times there won't be one specific formula, and you will have to be systematic and accounting for all future flows and discount them accordingly, manually.

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 \( PV = \text{\textdollar}18115.62 \).