Future Value

[tsd]

I am trying to run a future value out 35 years (a retirement calculation)
with all constants, except I want the "PMT" to be variable, specifically, I
want the payment to be 3% of my salary, indexed each year for inflation (I am
using 3.5%). This is not my actual savings, but instead a simulation comaring
the company's pension contribution versus a 3% contributuion to a 401k. So if
my salary is $100,000, in year one, PMT would be $3000, but in year two, PMT
would be $3105 (3% of 103,500) and so on. Any advice would be appreciated.
Thanks!

 

[Fred Smith]

The formula for the future value of indexed payments, where i is the
interest rate, and j is the indexing rate, is:

FV = ((1+i)^n - (1+j)^n)/(i-j)

Regards,
Fred.

 

[Fred Smith]

The future value of indexed payments, where i is the interest rate, and j is
the indexing rate, is:

= ((1+i)^n - (1+j)^n) / (i-j)

Regards,
Fred

 

[tsd]

Fred,

Thanks for getting back to me so quickly. You may need to dumb this down a
bit for me though. For some reason, after I imput your formula, Excel doesn't
recognize the rest. What does "n" stand for?

 

[Fred Smith]

Sorry, I thought you were familiar with financial functions. "n" is the
term -- in your case number of years to retirement, assuming you are using
annual payments.

Regards,
Fred.

 

[Fred Smith]

One more thing -- the formula I gave you is the future value factor -- ie,
how much payments of $1 per year indexed at j% will grow to at an interest
rate of i% for n years.

To get your future amount, multiply by your initial annual payment. The full
formula is therefore:

= PMT * (((1+i)^n - (1+j)^n) / (i-j))

Using your data of a initial payment of $3000, inflation at 3% and a 6% rate
of return over 35 years, you get:

= 3000 * (((1+.06)^35 - (1+.03)^35) / (.06 - .03))
= $487,222

Regards
Fred