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Need formula written out and step by step explanation. It helps to highlight the number and key words in the question so that I understand what is what.

Backdating Annuities

1. A \$1,000,000 lottery prize pays \$50,000 per year for the next 20 years. If the current rate of return is 4.5%, what is the present value of this prize?

2. An insurance policy offers you the option of being paid \$750 per month for 20 years or a lump sum of \$50,000. Which has the greater value if the current rate of return is 4.5% compounded monthly and you expect to live for 20 years?

3. Use the bond yield calculator to determine the yield of a bond that has 5 years to maturity (therefore ten semesters to go), has a coupon interest of 6% and a market price of \$102.5. Net Present Value and Venture Capital

4. Jim D’Addario of the well-known guitar and bass string factory D’Addario Strings in Long Island, NY, is considering two new designs for more efficient and higher quality machines (the company has won many manufacturing and product patents in the field). Assume machine A costs \$750,000 to make and is expected to return the following net earnings over five years, after which time it is retired: \$10 million, \$9 million, \$8 million, \$7 million, and \$6 million, respectively. Assume machine B costs \$850,000 to make and is expected to return the following net earnings over five years, after which time it is also retired: \$10.1 million, \$9.1 million, \$8.1 million, \$7.1 million, and \$6.1 million, respectively. All other things being equal, which design should Jim go with if he is using a discount rate of 7% Hint: Use NPV analysis.

5. Do some research and write a brief post on the general history of venture capital since the 1990s (maximum 600-700 words).