Present versus Future Values... Please write down an equation for each part. I do not need the solution (a numerical amount). You can assume that people discount the interest rate.

a. If I give you $30,000 today, and you invest it, how much money will you have in 25 years - assuming an interest rate of r? (Ignore inflation.)

b. Suppose you win the lottery! Starting next year, you will receive a payment of $100,000 per year for each of the next 20 years! What is the payment stream worth to you today - assuming an interest rate of 0.05? (Ignore inflation.)

c. If I promise you a payment of $50,000 in 15 years, what is it worth to you today - assuming an interest rate of r? (Ignore inflation.) Is it worth more or less than $50,000 today? Explain.

d. Scott wants to buy a new car. Suppose that Scott is offered a payment plan in which he will pay Pt in months t=1 to 24, where Pt covers principal borrowed and interest. Alternatively, Scott can pay a total of C in cash today (t=0) and make no additional payments. Assume that the interest rate is r. Assume that there is neither inflation nor deflation. What value of C will make Scott indifferent between paying C today and using the payment plan? (Provide an equation.)

e. Continuing with the situation described in d, what condition would make the payment plan a better option for Scott?