$($a$)$ An investor receives $$1,100$ in one year in return for an investment of $$1,000$ now.

Calculate the percentage return per annum with

$($i$)$ Annual compounding.

$($ii$)$ Semi$-$annual compounding.

$($iii$)$ Monthly compounding.

$($iv$)$ Continuous compounding.

$($b$)$ What rate of interest with continuous compounding is equivalent to $15\%$ per annum

with monthly compounding?

$($c$)$ A deposit account pays $12\%$ per annum with continuous compounding, but interest

is actually paid quarterly. How much interest will be paid each quarter on a $$10,000$

deposit?