Please walk me through on how to solve this:
A sum of $1000 is deposited in an account with an interest rate of r percent compounded monthly. At the end of 5 years, the balance in the account is given by:
$A= 1000(1+r/1200)^{60}$
Find the rate of change of A with respect to r for the following rates: a. r= 8% b. r= 10% c. r= 12%
So far, this is what I've come up with but I don't know if it's correct. Also, should it be $dA/dr$ ?
It's not an implicit differentiation problem. It is asked directly the variation of an explicit function. You did it well except for your equating $A'$ to $1$
$$\frac{\mathrm dA}{\mathrm dr}=1000·60\left(1+\frac{r}{1200}\right)^{59}\frac{\mathrm d}{\mathrm dr}\left(1+\frac{r}{1200}\right)=$$
$$=\frac{1000·60}{1200}\left(1+\frac{r}{1200}\right)^{59}=50\left(1+\frac{r}{1200}\right)^{59}$$
Now, this variation is to be calculated for some values of $r$. e.g.
$$\frac{\mathrm dA}{\mathrm dr}(8)=50\left(1+\frac{8}{1200}\right)^{59}\approx74.00$$