Explain (that means write an explanation) why the effective annual rate (EAR) differs from the APR.

You have decided you want to retire in 30 years from now. You want to live on a retirement of $90,000 per year. You figure you will live about 40 years on that retirement (you work-out on a regular basis, and live a healthy lifestyle). After 40 years of retirement, you plan to die (yes – all retirement planning has to make an assumption about when you die). While on retirement, you think you can earn 5% on investments. Between now and retirement, you think you can earn 8% on investments (you are more risk tolerant before retirement). We will work through this problem a step at a time.

a) How much will you have to have saved at retirement if you want to withdraw $7,500 per month (which is $90,000 per year) over 40 years of retirement, assuming the balance is earning 5% per annum? For simplicity, assume that you will pull out the $7,500 at the end of each month.

b) Now that you have calculated the amount you need to have at the moment you retire, let’s find out how much you will need to save each month to hit that target. What fixed amount would you need to save per month between now and retirement, in order to hit the amount you calculated in part a). Make sure these are contributed “?o and are compounding “?o monthly at an annual rate of 8%.

c) One last wrinkle to part b): if you wanted to buy a new car (for $60,000) and take a celebratory trip (for $45,000) the day after you retire, how much would you have to save on a monthly basis at 8% per annum, in order to do those two things and still get the income described in part a)?

Part II “?o Miscellaneous

d) If you wanted to save up so you could pay cash for a $225,000 house, and you felt like you could afford to save $950 per month, how many years and months would it take to save up all $225,000 if your savings earned 7.00% return per annum?

e) If a mortgage loan is advertised as costing 4.35% APR (and assuming no points or other fees), what would the effective annual rate (EAR) on that mortgage be (assuming you are making monthly payments)?


 

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