**Present value continuous compounding = C ÷ e**^{rt}

C = cash flow

r = rate

t = time

Present value of continuous compounding formula helps an investor to determine the current value of a future amount which is earning interest at continuous compounding rate. Here in the formula there are total three concepts time value of money, continuous compounding and present value of money.

## How continuous compounding formula derived

The formula for present value of continuous compounding wasderived from the future value of an interest bearing investment. Here is theformula written for future value of interest bearing account;

**Future value (FV) = PV × [1 + (i ÷ n)] ^{n × t}**

From the aboveequation if we calculate the limit of formula as ** n** approaches to infinitythen we get a more simplified version of this formula;

**FV = PV × e ^{i × t}**

Now we will discuss some basic concepts of present value,time value of money, and continuous compounding. So, that one can understandthe present value of continuous compounding precisely.

**Present value:**Time value of money plays the underlying role to bring-up the present valueconcept. Present value says that if a person has two options to receive anamount of $500 today vs. $570 after 5 years. Then to make precise decision andmake more profits he/she must have to calculate the value of $570 receivedafter 5 years at present time.

**Time value of money:**It is basically the idea that a specific amount available today will worth morethan the same amount available after 2 years. The underlying concept for thatis inflation because prices changes over time and thus the currency devaluesover time. For example, if $500 is received today it will worth more than $500received after 2 years.

**Continuouscompounding: **Continuous compounding concept says that the compounding isconstant. While ordinary compounding have a compound basis like annual, semi-annual,monthly, or quarterly. But continuous compounding is constant and exhibits aninfinite level of compounding within a specific time.

### Present value continuous compounding formula example

Let’s suppose that a person is expecting to receive $1800from an interest bearing account after 2 years. The continuous compounding rateof return is 7% and you have to calculate the current amount required to reachthe target balance within 2 years. Now putting values in the formula;

PV = 1,800 ÷ e^{(0.07)× (2)}

PV = $1,564.84

So, now one can see that, the person will require to invest $1,564.84today to receive $1,800 after 2 years with continuous compounding interest rateof 7%.