Imagine you are a financial advisor to Valerie VanNess. Ms$.$ VanNess wants to retire in $25$

years. She wants to start saving an annual amount at the end of each year until she retires. She

expects to live for another $20$ years after she retires. During retirement she wants to withdraw

$$15,000$ at the start of each year from a savings account. She can earn $10\%$ per year on

balances in this savings account

a$.$ Write out the formula that calculates the $PV$ of regular

annuity.

If you use the PV annuity formula, at what

time$/$year is the PV placed? Write out the formula that calculates the FV of a regular

annuity.

When the FV is calculated, in what year is the

FV placed

b$.$ How much will Ms$.$VanNess have to deposit in the savings account at the end of each

year for the next $25$ years, if the interest rate is $10\%,$ compounded annually?

c$.$ How would the lyearly deposits be changed if Ms VanNess expects her cat to live for

another five years after her death, and she wants to leave an amount in an account that

will be used to pay the cat sitter $$5500$ at the start of each year, for those five years.

$($Draw a new timeline, or add to your timeline above$).$