Formula for FV of non-interest-bearing account given annual contributions increase at x% compounded rate

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

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

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

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

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

-- Joe

Yes, I was in error. Thanks for catching that.

-- Joe