This diagram is useful to explain the difference between present value and future value in financial mathematics.

This video will help you understand the difference between present and future value.

The difference between present and future value is one of the hardest things for beginning students to understand.

**Future values** are the same as compound values where we are looking into the future and working out the value of an investment left earning interest and the interest is continually added to the principal amount for reinvestment.

**Accumulated Value (S) = P (1 + i) ⁿ**

**Where**

** P = Principal**

** i = interest rate for each period**

** n = the number of periods**

**Present values** are where we have a sum of money in the future and we want to know what it would be worth in today’s dollars.

The formula we used for compounding can also be used and rearranged to find the initial principal.

**Accumulated Value (S) = P (1 + i) ⁿ**

**Where**

** P = Principal**

** i = interest rate for each period**

** n = the number of periods**

We can rearrange the formula to find P (the **principal**) when we know what the **accumulated value** (S) is.

** S = P (1 + i) ⁿ**

__ S __ = P

**(1 + i) ⁿ**

**S (1 + i)¯ⁿ = P**