How much would one have after 55 years at 2 percent per year compound interest on an intial deposit of $1000?

We must use the formula for annual compound interest as follows:

 `A=P(1+(R/100))^n`

In this formula, P is the initial invested amount, R is the interest rate, n is the number of years, and A is the final amount.

We are given the following information: The initial deposit is $1000 (P = 1000). The interest rate is 2% (R = 2). The money is invested for a period of 55 years (n = 55). 

Plugging all this into the formula above yields:

`A=1000*(1+(2/100))^55=2971.73`

So, an initial investment of $1000, compounded annually at a rate of 2%, for a period of 55 years, would result in a final balance of $2971.73

Note that if the interest were compounded over a different time period (say monthly or half-yearly), you would have to use the following formula, 

 `A=P=(1+((r/100)/n))^(n*t)`

where t is the number of years and n is the number of time periods per year.