|
Posted by Joe D. on February 2, 2007, 1:25 pm
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.
|
|
Posted by kastnna on February 2, 2007, 1:54 pm
> 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.
Wouldn't 5% compounded growth be 100, 105, 110.25 (not 105.25),
115.76, etc?
|
|
Posted by Joe D. on February 2, 2007, 7:15 pm
>
> Wouldn't 5% compounded growth be 100, 105, 110.25 (not 105.25),
> 115.76, etc?
>
Yes, I was in error. Thanks for catching that.
-- Joe
|
|
Posted by woessner@gmail.com on February 2, 2007, 2:00 pm
> - # of years
> - initial account value
> - initial annual deposit amount
> - % annual compounded increase of annual deposit
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
|
|
Posted by Joe D. on February 2, 2007, 7:15 pm
Bill/Dave thanks so much for the help. That's exactly what I needed.
-- Joe
|
| Similar Threads | Posted | | Annual rate of return on 403B | January 10, 2007, 4:25 pm |
| Hi-rate online savings account allowing 3 owners? | September 6, 2008, 3:08 pm |
| Which free cash flow formula | March 6, 2008, 7:45 am |
| Social Security retirement delay credit not compounded | December 12, 2007, 12:00 pm |
| Annual Gift tax exclusion | March 8, 2007, 11:45 am |
| 529 contributions and withdrawals | November 9, 2006, 11:17 am |
| free "annual" credit reports... | October 22, 2006, 7:09 am |
| Roth IRA contributions after retirement | January 29, 2008, 4:50 pm |
| Comingling pre-/post-tax contributions in IRAs? | September 6, 2007, 12:56 pm |
| Roth and IRA contributions without earned income? | March 25, 2008, 5:31 am |
|
|
Yahoo! 
Google 
Windows Live 
del.icio.us 
digg 
Netscape 
XML Sitemap