calc: Future Value
8.6.2 Future Value
------------------
The ‘b F’ (‘calc-fin-fv’) [‘fv’] command computes the future value of an
investment. It takes three arguments from the stack: ‘fv(RATE, N,
PAYMENT)’. If you give payments of PAYMENT every year for N years, and
the money you have paid earns interest at RATE per year, then this
function tells you what your investment would be worth at the end of the
period. (The actual interval doesn’t have to be years, as long as N and
RATE are expressed in terms of the same intervals.) This function
assumes payments occur at the _end_ of each interval.
The ‘I b F’ [‘fvb’] command does the same computation, but assuming
your payments are at the beginning of each interval. Suppose you plan
to deposit $1000 per year in a savings account earning 5.4% interest,
starting right now. How much will be in the account after five years?
‘fvb(5.4%, 5, 1000) = 5870.73’. Thus you will have earned $870 worth of
interest over the years. Using the stack, this calculation would have
been ‘5.4 M-% 5 <RET> 1000 I b F’. Note that the rate is expressed as a
number between 0 and 1, _not_ as a percentage.
The ‘H b F’ [‘fvl’] command computes the future value of an initial
lump sum investment. Suppose you could deposit those five thousand
dollars in the bank right now; how much would they be worth in five
years? ‘fvl(5.4%, 5, 5000) = 6503.89’.
The algebraic functions ‘fv’ and ‘fvb’ accept an optional fourth
argument, which is used as an initial lump sum in the sense of ‘fvl’.
In other words, ‘fv(RATE, N, PAYMENT, INITIAL) = fv(RATE, N, PAYMENT) +
fvl(RATE, N, INITIAL)’.
To illustrate the relationships between these functions, we could do
the ‘fvb’ calculation “by hand” using ‘fvl’. The final balance will be
the sum of the contributions of our five deposits at various times. The
first deposit earns interest for five years: ‘fvl(5.4%, 5, 1000) =
1300.78’. The second deposit only earns interest for four years:
‘fvl(5.4%, 4, 1000) = 1234.13’. And so on down to the last deposit,
which earns one year’s interest: ‘fvl(5.4%, 1, 1000) = 1054.00’. The
sum of these five values is, sure enough, $5870.73, just as was computed
by ‘fvb’ directly.
What does ‘fv(5.4%, 5, 1000) = 5569.96’ mean? The payments are now
at the ends of the periods. The end of one year is the same as the
beginning of the next, so what this really means is that we’ve lost the
payment at year zero (which contributed $1300.78), but we’re now
counting the payment at year five (which, since it didn’t have a chance
to earn interest, counts as $1000). Indeed, ‘5569.96 = 5870.73 -
1300.78 + 1000’ (give or take a bit of roundoff error).
Info Catalog
calc: Percentages
calc: Financial Functions
calc: Present Value