Kendra is $25$ years old. Her salary now is $$47,000$ per year, and she expects raises with inflation. Inflation is expected to be $2\mathrm{.}5\%,$ and Kendra has access to a retirement investment plan that has an average return of $8\%.$ Kendra plans to retire at age $67$ with a RLE $=20$ years. Kendra's wage replacement ratio is $100\%,$ and she does not plan on receiving Social Security.

a$.$ How much money must Kendra have in savings at age $67$ to retire at her desired standard of living?

b$.$ What is the present value $($now$)$ of Kendra's retirement need?

c$.$ How much must Kendra invest annually until age $67$ to meet her goal?