$($a$)$ Compute the amount a borrower must repay per month, given a mortgage

loan having principal $500,000$ Euro, a fixed monthly interest rate of $0\mathrm{.}5\%$

and a term of $10$ years.

$($b$)$ Find the present value of a growing annuity, lasting $12$ years, having

payments which begin at $1,000$ Euro in the first year and grow at a rate

of $3\%$ annually thereafter, and subject to an interest rate of $6\%$ annually

$($c$)$ Find the present value of a perpetual revenue stream having flow rate

$R(t)=t+2,$ which is subject to a fixed interest rate of $3\%.$