1) Answer the following questions:

a. Find the present value of a $1,000 payment that happens 5 years from now if the annual interest rate is 3.5%

b. If you invest $1,000 today at an interest rate of 2.0%, how much will you have in 30 years?

c. If an investment costs $6,000 today and it earns $2,500 at the end of each of the next 3 years, what is the net present value of the project if the interest rate is 10%?

2) Suppose you own a share of stock that is expected to pay out $100 in dividends at the end of each of the next 30 years. First, write out an expression for the present value of this stream of income, then find the present value using the tools we developed in class.

3) Consider the following investment options:

Option 1: invest $100 now and get back $60 in six months $75 in a year, and $90 in 18 months

Option 2: invest $75 now and get back $10 per month at the end of each of the next 18 months

a. If the monthly interest rate is 0.80%, calculate the net present value of each option?

b. Which option would you choose first if your objective was to maximize the net present value of your investments? Explain why.

c. Which option would you choose first if your objective was to maximize the net present value of your investments per dollar spent? Explain why.

4) Consider the problem of whether or not to buy or lease a new piece of equipment. You know you only need it for 3 years, and you can purchase it or lease it.

The lease requires a down-payment of $2,000 upon signing the lease and then a monthly payment of $560 due at the end of each month for the next 5 years. At the end of the lease the equipment goes back to the dealer.

If you purchase the equipment you buy it for $35,000 in cash, and at the end of the 5 years you will sell the equipment for $5,000.

Assume the monthly interest rate is 0.5%. Calculate the present discounted value (cost) of your options of leasing or buying this piece of equipment. Which option should you take?