$($Due APRIL $20$ at $11$:$55$pm$)$

Find a house that is on the market in YOUR HOMETOWN $($addres $112$ Hart Rd$,$ Guilford,CT $06437.$ price $389,900),$ If you put $20\%$ down pay and loan the rest by $30-$year fixed rate mortgage.

$($a$)$ If the current rate is $5\mathrm{.}5\%,$ what is your monthly payment?

$($b$)$ How much interest will you pay over the term of the loan?

$($c$)$ If you pay $$500$ more every month with the same rate, how much total interest can you save? $($Hint: you will pay off the loan quicker.$)$

$($d$)$ If the house price increases $3\%$ per year, how much does the house worth after $30$ years?

$($e$)$ If you do not buy the house, instead you save the amount of money in $($a$)$ into an annuity account every month for $30$ years with a saving interest rate $2\mathrm{.}5\%$ compounded monthly. How much money will you have in that annuity account after $30$ years? Note, the $20\%$ down pay will be the starting value $($PV$)$ of the annuity account. How much total interest are you going to gain?

$($f$)$ Based on the above calculation, which is better investment, the house or saving annuity?

$($g$)$ Is there anything else we should consider when we compare these two investments?

You need to show all your work. When you use $\text{'}$TVM Solver', you need to show all your input, e$.$g$.N=,I\%=,PV=,PMT=,FV=,\frac{P}{Y}=,\frac{C}{Y}=.$