Why does the benefit of using margin diminish over time?

When using margin to invest, your exposure is increased but there are fees associated with doing so. The future value of an investment given an annual return rate and margin loan interest rate can be calculated using:

p*l*(1+r)^n-sum i*p*(l-1)*(1+r)^k, k=0 to n-1

where p is the principal, r is the annual return, l is the leverage factor (ie. 2 would mean half the money is borrowed), n is the number of years the investment is held and i is the interest rate on the loan. For simplicity, interest is paid at the end of the year.

I have two questions:

1. Is this formula correct?
2. Why does the annualized return tend towards r as n increases? For example:

when n is 3 (and p is 1, l is 1.6, i is 0.03, r is 10%…)

(1.6*(1+0.1)^3-sum 0.03*(1.6-1)*(1+0.1)^k, k=0 to 3-1)^(1/3)=1.274

when n is 10000

(1.6*(1+0.1)^10000-sum 0.03*(1.6-1)*(1+0.1)^k, k=0 to 10000-1)^(1/10000)=1.1

It seems confusing that the benefit of using leverage diminishes the longer the holding period (if the math is correct).

Edit: I think the original loan amount must be subtracted from the future value.