Let's assume we want the present value of $5,000, which we will receive six months from now,
assuming an 8% interest rate. We know that the present value will be less than $5,000.
Using a table:
You can find a "present value of a lump sum" table by going to principlesofaccounting.com
and clicking "supplements" at the bottom-left of the screen. "Time value of money"
will be one of the supplements listed.
You will use the table called "Present Value of $1." Because we are interested in a payment
six months from now, we will have to divide the interest rate by 2 to represent a half-year.
Looking at 4% for 1 period, we get a factor of .96154.
Multiply the $5,000 by this factor.	$4,807.70
Using a mathematical formula:
Here, the formula will be the principal amount (1 plus the interest rate) to the power of the time period.
In Excel, the math symbol for "to the power of" is ^
The interest rate is the full 8% and the time period is 0.5 years. When we want present
value, we will enter the power of as negative because we are discounting the principal amount
backwards. If we were calculating future value, the time period would be positive.
Formula is 5000*(1+.08 )^0.5	$4,811.25
Notice this comes out slightly different.
This is because some calculations use 360 days and some use 365.
We can mostly correct for this by multiplying the period by 365 and dividing by 360.
Formula is 5000*(1+.08 )^(0.5*365 360)	$4,808.68
Using the Excel formula:
The present value formula is =PV(rate, periods, amount)
The rate must be divided by 2 because it is a half-year.
You will get a negative answer as a result because the formula is used to ask, "What amount do I
need to invest now (negative cash flow) to get a certain amount in the future?"
=PV(.08 2,1,5000)	($4,807.69)
If you are preparing a spreadsheet and you need the number to display as positive,
simply put a negative in front of the amount in the formula
=PV(.08 2,1,-5000)	$4,807.69