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 $$\mathrm{Var}(FV)≈\sigma^2\times(g′(μ))^2.$$

I want to compute the variance of $FV =A\sum_{k=1}^n(1+r)^k=:g(r)$, assuming interest rate $r\sim\mathrm{N}(\mu,\sigma^2)$ and constant equal payments $A$. As discussed in the comments, the Delta Method gives an approximation $\mathrm{Var}[FV]≈\sigma^2\times(g′(\mu))^2$. Is there a way to get an exact answer?

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 $$Var(FV)≈σ2×(g′(μ))^2.$$

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 $$\mathrm{Var}(FV)≈\sigma^2\times(g′(μ))^2.$$

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

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 $$Var(FV)≈σ2×(g′(μ))^2.$$