How does the present value of a lump sum compare to the present value of an annuity?

Part one:
Answer these questions (for quantitative questions, show your work):

How does the present value of a lump sum compare to the present value of an annuity?

How does the future value of an ordinary annuity compare to the future value of an annuity due?

How does the present value of an annuity compare to the present value of an annuity due?

What?s the value today of $500 received in 3 years if the going rate of interest is 10% per year?

An individual has $3,000 today. What will that be worth in 7 years if the going rate of interest is 4% per year?

What?s the present value of $250 received at the end of each year for the next 8 years if the interest rate is 4.5% per year?

Length: 1-2 pages.

Part two:

Here is your opportunity to dream! Choose a vacation destination anywhere in the world (to which you must fly) for a two week trip (assume you have vacation time from work to take the trip) that you would like to take exactly ten (10) years from today. This can either be an individual vacation, a couple trip or a family excursion, depending on your life circumstances. After you?ve picked your destination (dream big), determine the following:

Travel expenses for all members of the group
Lodging expenses for the entire time period of the trip
Estimate of daily food expenses
Make a list of activities that you would like to engage in every day of the trip. Determine a cost for each day?s activity list (for example, tickets to amusement parks, museum entrance fees, boat trips, scuba diving, deep sea fishing, entertainment venues, etc.)
Make a list and associated cost estimate of any other expenses that you believe should be included in a total cost estimate for your vacation (e.g., pet boarding, house sitting, airport parking fees, etc.)
Would only someone who makes a high income be able to afford this trip? Or would someone who makes the minimum wage be able to afford this trip?
NOTE: You must research all aspects of your list to substantiate your cost estimates; that is, you must demonstrate and/or document how you derived each cost estimate in the list.

After gathering and organizing all collected data, prepare a document describing your destination (including your reason for choosing that location), listing (and substantiating) all costs of the trip (this can be done in a table or bullet point format, but it must be clear and provide sufficient detail so that the reader understands your interest and passion for your vacation), and determining a total cost of your dream vacation from the time you leave to the time you return.

Assuming that your estimated total cost will grow by 2.5 percent per year (due to inflation), demonstrate how you would compute the expected future cost of your dream vacation.

Suppose that you can invest money every month into a fee free mutual fund and that this fund is expected to have a 10 percent nominal annual rate of return. Using your estimated future cost (including inflation) as a future value, determine the amount of money you must save each month for the next 10 years (i.e., 120 months) to achieve your goal. Then determine the monthly amount you must save if you delay your trip for an additional five years (that is, you will take the trip 15 years from today = 180 months) instead of 10 years from today (note: be sure to add 5 additional years of inflation to the estimated future cost). Write an explanation for your calculations so the reader is completely clear on how you derived your required monthly deposits.

Based on this numerical representation of your dream vacation, write a well contemplated critical analysis of your trip. For example, explore questions such as: is this something that you think is worth saving for, have you changed your mind after seeing the reality of the required sacrifice, are you rethinking the location or luxury level of your accommodations or daily outings, and so on.

Note that you must properly cite all reference sites that you used to collect data to estimate your costs value, etc.

Length: 4-5 pages not including title page and references

Your response should demonstrate thoughtful consideration of the ideas and concepts presented in the course and provide new thoughts and insights relating directly to this topic. Your response should reflect scholarly writing and current APA standards.