Answer
The continuous compounding at the rate of $5.6\%$ does not yield the required amount. The other bank offers a better deal.
Work Step by Step
The formula for the amount $A$ after $t$ years due to a principal $P$ invested at an annual interest rate $r$ compounded $n$ times per year can be computed as:
$A=P(1+\dfrac{r}{n})^{nt}$
When the compounding is continuous, use the formula $A=Pe^{rt}$
We need to compute with continuous compounding. Thus, we use the formula: $A=Pe^{rt}(1)$
We are given the information:
$r=0.056 ; t=1; P=1000$
Plugging this in yields the amount after $1$ year:
$ A=1000e^{(0.056)(1)}=\$ 1057.60,$
This amount is not enough because the required amount is $\$ 1060$.
The other bank offers $r=0.059$, compounded $n=12$ times per year:
Thus, we have: $A=1000 (1+\dfrac{0.059}{12})^{12}=\$ 1060.62$
So, this is a better deal than the first bank.
