Please solve problem step by step and write out each formula used to solve the problem. Thank you PMT

$2.$ You plan to retire in $30$ years and plan on saving $$15,000$ annually, starting next year, for the next $30$ years. You expect to need $$\frac{1}{b}ar(2)0,000$ about $18$ years from now for college tuition for your recently born daughter which must be paid out of these savings. You expect to live $35$ years during retirement $($the first retirement payment will be $31$ years from today$).$

a$.$ If you assume an interest rate of $8\mathrm{.}15\%$ over the entire period, how much will you have available te spend annually in retirement in assuming you plan to purchase a $$200,000$ summer retirement home five years after you retire $($the purchase will be made in year $35)?$

b$.$ Same as part a$,$ except that interest rate is $5\%.$ Does your retirement quality of live improve significantly? Assume the same college tuition and retirement home price.

c$.$ If interest rate is $5\%,$ but you want to keep the same retirement quality of life as if the interest rate is $8\mathrm{.}15\%.$ How much extra money do you need to save annually?