I am trying to compute, until now with no luck, the variance of $$ \sum_{y=1}^n{ A*(1+r)^{y} } $$ which is equivalent to

$\frac{(1+r)[(1+r)^{y}-1]}{r}*A$,

Where we assume $$ r \sim N(\mu,\sigma^2)$$

A is a constant.

Thanks

EDIT :

Following @Zen, we could approximate $$Var(FV)≈σ2×(g′(μ))^2.$$