Ignore income tax. Using excel.

5. Annuities Due Remember, annuities due are amounts paid at the beginning of each period.

a. Future values

i. You decide to place $200 at the beginning of each month in an investment account earning interest at 4.33% annually (4.33% / 12 monthly). You plan on following this practice for five years (60 months). How much will you have accumulated in the account at the end of the five-year period?

ii. An investor invests $100 an account that returns 5% annually (5% / 12 per month). How much is the investors account worth at the end of the five-year period?

b. Present values

i. Assume you are able to purchase a financial instrument (an annuity) that will pay you $400 on the first day of each month for the next five years. Ignoring any problems of collectability and assuming 7.21% annually (7.21% / 12 monthly) is a proper discount rate, how much should you pay for this financial instrument if you want to purchase it?

ii. Using the financial instrument above again, if the discount rate changes to 9.50% annually, what is the new purchase price?

iii. An owner of a building wishes to sell his rights to a stream of rental payments due on the first day of each month for the next two years. The monthly payments total $4,500 and the correct annual discount rate is 4.75% (4.75% / 12 per month). How much should the building owner be able to charge for the stream of payments (i.e. for the annuity)?

c. Retirement planning (an application of future values)

i. Assume you make annual contributions to a Roth IRA of $1,250 per year beginning on your 25th birthday. Assume further that the account is projected to earn an annual return of 7.15% and that you will retire on your 65th birthday. What is the projected balance in the account on the date of your retirement? Assume no contribution on your 65th birthday. In other words, the last contribution occurs at the beginning of the 40th year, on your 64th birthday.

ii. Assume you begin making the contributions above on your 35th birthday, rather than your 25thbirthday, but double the annual contribution to $2,500. What is the projected balance in the account on the date of your retirement?