1. Calculating PV Using Compound Interest
Let's figure out how to calculate the present value when we know the
future value using compound interest. This process is called discounting,
as we are discounting their future value in order to find their present
value. Let's say we need 115.76 in three years time, and the interest
rate is 5% per year. So what do we need to start with
today? So instead of multiplying forward from the present value to the future
value, we'll do the opposite. We'll divide to go backwards from the future
value to the present value. Starting with the future value of
115.76 we divide by one plus 5% three times to find the present
value of $100. We can write this as a formula. The present value
equals this future value divided by one plus 5%
and since we're dividing three times, we raise this denominator to the power
of three. In general terms, the formula looks like this. The present value
equals the future value divided by[one plus the interest rate close bracket,
all raised by n, the number of years. In math, dividing by a
term is the same as multiplying by its inverse. So this formula can
also be written as this. The present value equals the future value multiplied
by one over bracket one plus the interest rate]
again, all raised to the power of n, the number of years.
Let's double check these results in Excel and introduce a couple of very
useful Excel functions.
2. Let's practice!