$1.$ Mr$.$ Kolosa has invested K$100,000$ for $5$ years at $10\%$ rate of interest.

$($a$)$ What will be the simple interest and amount after $5$ years?

$($b$)$ What will be the compound interest and amount after $5$ years if interest is paid $($i$)$ Monthly,

or $($ii$)$ Quarterly?

$($c$)$ What should be annual compound interest rate to make the amount K$200,000$ after $5$ years?

$2.$ How long should any sum of money be left on deposit at $4\mathrm{.}5\%$ APR if the value of the deposit is

to increase by $70\%?$