$1$.The compound interest on certain sum for $2$ years is $\$410$ and simple interest is $\$400$. Find the rate of interest per-year.
$2$.A sum of money invested at compound interest amounts in 3 years to $\$ 2400$ an in $4$ years to $ \$ 2520$. Find the rate of interest per-year.
Solving them using the traditional compound interest formulas is a bit tedious for me under exam conditions,so please suggest if there is any kind of short-cut procedure to solve them.