Question

Ten years from now, you plan on taking a year's unpaid biking across the US from d vacation an Phifadefphra to San Diego. You estimate that expenses, e.g. hotels, bike repairs, food, tolls, etc, Will be $5,000 per month over the 12-month journey. The interest rate is 8.4%, compounded monthly. Hint: draw a timeline! 

a) what is the appropriate annuity discount factor in this problem during the 12-month journey? 

b) How much money will you need in the bank at the start of your trip (in year 10) in order to withdraw $5,000 per month for expenses during your trip? 

c) What lump sum of money should you deposit in the bank today (year 0) so that you will have enough money ten years from now for your trip? Don't forget that the interest rate is 8.4% compounded monthly. 

d) Suppose, instead, that you want to start saving now to insure that you have sufficient funds for the trip you will take in ten years. How much should you deposit monthly in order to do this?  

Answer 1

Answer a.

Annual Interest Rate = 8.4% compounded monthly
Monthly Interest Rate = 8.4%/12 = 0.70%
Duration = 12 months

Annuity Discounting Factor = PVIFA(0.70%, 12)
Annuity Discounting Factor = (1 - (1/1.007)^12) / 0.007
Annuity Discounting Factor = 11.47138

Answer b.

Monthly Expense = $5,000
Duration of Trip = 12 months
Annuity Discounting Factor = 11.47138

Amount needed at the start of trip = $5,000 * Annuity Discounting Factor
Amount needed at the start of trip = $5,000 * 11.47138
Amount needed at the start of trip = $57,356.90

So, in the beginning of trip $57,356.90 is required.