"kastnna" <kastnna[at]auburnalum.org> wrote in message
news:1170442464.350469.250770[at]v45g2000cwv.googlegroups.com...
- quote -


-- Joe

Bill/Dave thanks so much for the help. That's exactly what I needed.

-- Joe

On Feb 2, 12:25 pm, "Joe D." <nos...[at]invalid.invalid> wrote:
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Assuming that the initial balance in the account is I, that deposits
of amount D are made on the last day of the year, the balance on the
last day of the Nth year is


D [(1+r)^N - 1]
B = ------------------------ + I - D
r

Examples: With initial balance $1000 and deposits of $100 growing at a
5% compounded annual rate:

After 1 year, you would have B = 100*(1.05^2-1)/.05 + 1000 - 100 =
$1,105

After 90 years, you would have B = 100*(1.05^90 - 1)/.05 + 1000 - 100
= $160,360.73

Hope this helps.

Dave

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This is the same thing as the annuity formula in reverse. Instead of
adding interest to older deposits, you're making newer deposits
larger. Conceptually, you've reversed the order of the summation, but
that doesn't matter.

Let T be the number of years, D be the initial annual deposit and r be
the rate at which the deposits increase and F be the future value.
Then you want:

F = D + D(1+r) + D(1+r)^2 + ... + D(1+r)^(T-1)
F = D(1 + (1+r) + (1+r)^2 + ... + (1+r)^(T-1))
F = D * (1 - (1+r)^T) / (1 - (1+r))
F = D * (1 - (1+r)^T) / -r
F = D * ((1+r)^T - 1) / r

Since the initial account balance isn't earning interest, you can just
add it to the formula above.

--Bill

- quote -


Wouldn't 5% compounded growth be 100, 105, 110.25 (not 105.25),
115.76, etc?

I'm trying to find the formula to calculate the final value of a
non-interest-bearing account, given annual deposits which increase at x%
compounded rate. Would appreciate any help.

Inputs:

- # of years
- initial account value
- initial annual deposit amount
- % annual compounded increase of annual deposit

E.g, initial account value is $1000, it's non-interest bearing so stays
constant except for deposits.

Initial annual deposit is $100, which increases at a 5% compounded annual
rate (next year's deposit would be $105, the following would be $105.25,
etc).

This continues for, say, 90 years what's the account final value? Just
looking for the formula.