ASG #$1$ Present Value and Future Value of Annuities

Spring $2024$

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.

Please look up the meaning of an "annuity due".

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?

Draw a timeline that clearly labels:

a$)$ Now

b$)$ The date Ms$.$ VanNess will retire.

c$)$ The date Ms VanNess will stop withdrawing from the savings account.

d$)$ The yearly amounts she will withdraw $($you do not need to draw the total number of withdrawals, but can indicate it somehow$).$

What is the Present Value of the withdrawals $($that occur at the start of each year$)$ that Ms$.$ VanNess plans to make while she is retired? Show all work

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?

How would the yearly 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$).$

Show all work. Explain calculations. Make clear any assumptions you feel necessary.