Present values are where we want to know what a sum of money in the future is worth in todays money.
In other words, we pull the future sum back to a now (year 0) value.
This diagram is useful to explain the difference between present value and future value in financial mathematics.
The formula used for compounding can also be used to find the initial principal.
This formula is rearranged to find the initial principal of an accumulated sum.
From the compound interest formula we know:
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.
Let’s look at these examples
What is the present value (value today) of $5,000 when;
1. Interest is 2.5% and the money is received in 8 years time?
5,000 x (1 + i)¯ⁿ
5,000 x (1.025) ¯ⁿ where n = 8
5,000 x .8207 = $4,103.50
2. Interest is 10% and the money is received in 6 years time?
5,000 x (1 + i)¯ⁿ
5,000 x (1.1) ¯ⁿ where n = 6
5,000 x .5645 = $2,822.50
With a knowledge of present value, you can calculate the present value of several sums and calculate the total present value.
You use this analysis when you calculate the Net Present Value and the Internal Rate of Return when analysing projects for viability.
