Answer the following questions:

1. What is the difference between an annuity and a perpetuity? (10 points)

2. What is the difference between an ordinary annuity and a past due annuity? (10 points)

Part ii

Find the required value for each problem. Show the formula used and the computations for each problem.

1. Carlos Matos has the opportunity to make an investment that requires a payment of $ 850 per year for the next ten years. If the investment is made at an interest rate of 7.5%, what is the value of that investment today?

2. What is the present value of an investment that guarantees a payment of $ 20,500 per year for the next five years if the annual compound interest rate is 12%?

3. Roberto Alomar is planning to invest $ 35,000 annually for the next six years, an investment that will pay him a compound annual interest of 10.5%. How much money will Roberto have at the end of the six years?

4. Cecilia Thomas is 27 years old and is planning to invest $ 5,000 annually in an IRA that pays 9.75% compound interest annually, until she retires at 65 years of age. How much money will Cecilia have for her retirement?

5. How much would you pay today for a perpetuity of $ 2,000 per year if the prevailing interest rate is 6.25%?

6. For how much would you buy a preferred stock that pays $ 6 in annual dividend if it requires a yield of 14% annual interest?

7. Determine how much you would pay in total, interest and principal, at the end of your 30-year mortgage at 3.99% compounded monthly, if the monthly payment is $ 775.00.

8. How much would you have to pay monthly for the car you want to buy if the cost of the car is $ 40,000 and they finance it at 5.55% compound interest for six years without having to pay soon?

9. How much money will you have paid at the end of ten years if you pay $ 12,000 for an equipment lease at the beginning of each year and the annual compound interest rate is 4.5%?

10. From the previous exercise, calculate how much you will pay at the end of the ten years, if you pay $ 10,000 annually at the end of each year instead of at the beginning of the year. Which option is best for you?