At an annual effective interest rate of i, i > 0, the following are all equal: (i) the present value of 10,000 at the end of 6 years; (ii) the sum of the present values of 6,000 at the end of year t and 56,000 at the end of year 2t; and 60 THE BASICS OF INTEREST THEORY (iii) 5,000 immediately. Calculate the present value of a payment of 8,000 at the end of year t 3 using the same annual effective interest rate.

Your goal is to have $2,000,000. you have a total of $40,000 today. you invest the $40,000 and want to add to it each month. at 10% annual interest, how much do you need to invest each month in order to bring the total up to $2,000,000 30 years from now?

The management of a private investment club has a fund of $250,000 earmarked for investment in stocks. to arrive at an acceptable overall level of risk, the stocks that management is considering have been classified into three categories: high risk (x), medium risk (y), and low risk (z). management estimates that high risk stocks will have a rate of return of 15%/year; medium risk stocks, 10%/year; and low risk stocks, 6%/year. the amount of money invested in low risk stocks is to be twice the sum of the amount invested in stocks of the other two categories. if the investment goal is to have a rate of return of 9% on the total investment, determine how much the club should invest in each type of stock. (assume that all the money available for investment is invested.)

Suppose the marginal damage and marginal benefit curves in a polluted neighborhood are md = p/3 and mb = 4 – p. also, suppose that transactions costs are low, so that the consumers and the firm can bargain. we saw that in this case, the socially-optimal level of pollution is achieved. start by computing the socially-optimal p. then, for each of the following cases, compute the amount of money transferred through the bargaining process, and indicate who pays whom (i.e., whether consumers pay the firm, or vice versa). also, compute the gains to each party relative to the status quo (i.e., the starting point of the bargaining process).a)consumers have the right to clean air; firm is dominant in the bargaining process.b)consumers have the right to clean air; consumers are dominant in the bargaining process.c)firm has the right to pollute; firm is dominant in the bargaining process.d)firm has the right to pollute; consumers are dominant in the bargaining proces