(a) If you deposit money continuously at a constant rateof $1000 per year into a bank

In Exercises 17 give an expression that represents the statement. Do not simplify your expression. The future value of single $C deposit, after 25 years, at a 3% interest rate compounded annually.

In Exercises 17 give an expression that represents the statement. Do not simplify your expression. The present value of $C deposited 25 years from now, at a 3% interest rate compounded annually

In Exercises 17 give an expression that represents the statement. Do not simplify your expression. The present value of a deposit of $C, made 5 years from now, with a 3% interest rate compounded continuously

In Exercises 17 give an expression that represents the statement. Do not simplify your expression. The present value of an income stream paying C dollars/year for a period of 15 years, at a 2% interest rate compounded continuously.

In Exercises 17 give an expression that represents the statement. Do not simplify your expression. The future value at the end of 15 years of an income stream paying C dollars/year throughout the 15 years, at a 2% interest rate compounded continuously.

In Exercises 17 give an expression that represents the statement. Do not simplify your expression. The future value, at the end of C years, of a series of three $500 deposits, where the first deposit is made now, the second a year from now, and the third two years from now. Assume a 2% interest rate compounded continuously.

In Exercises 17 give an expression that represents the statement. Do not simplify your expression. The continuous interest rate for a deposit $C that will grow to $25,000 in 30 years

Find the future value of an income stream of $1000 per year, deposited into an account paying 8% interest, compounded continuously, over a 10-year period.

(a) Find the present and future values of a constant income stream of $100 per year over a period of 20 years, assuming a 10% annual interest rate compounded continuously. (b) How many years will it take for the balance to reach $5000?

Find the present and future values of an income stream of $2000 a year, for a period of 5 years, if the continuous interest rate is 8%.

A person deposits money into a retirement account, which pays 7% interest compounded continuously, at a rate of $1000 per year for 20 years. Calculate: (a) The balance in the account at the end of the 20 years. (b) The amount of money actually deposited into the account. (c) The interest earned during the 20 years.

Exercises 1214 concern a single deposit of $10,000. Find the continuous interest rate yielding a future value of $20,000 in the given time period. 60 years

Exercises 1214 concern a single deposit of $10,000. Find the continuous interest rate yielding a future value of $20,000 in the given time period. 15 years

Exercises 1214 concern a single deposit of $10,000. Find the continuous interest rate yielding a future value of $20,000 in the given time period. 5 years

Exercises 1517 concern a constant income stream that pays a total of $20,000 over a certain time period with an interest rate of 2% compounded continuously. Find the rate at which money is paid, in dollars/year, and the future value of the stream at the end of the given time period. 5 years

Exercises 1517 concern a constant income stream that pays a total of $20,000 over a certain time period with an interest rate of 2% compounded continuously. Find the rate at which money is paid, in dollars/year, and the future value of the stream at the end of the given time period. 10 years

Exercises 1517 concern a constant income stream that pays a total of $20,000 over a certain time period with an interest rate of 2% compounded continuously. Find the rate at which money is paid, in dollars/year, and the future value of the stream at the end of the given time period. 20 years

Find a constant income stream (in dollars per year) which after 10 years has a future value of $20,000, assuming a continuous interest rate of 3%.

Draw a graph, with time in years on the horizontal axis, of what an income stream might look like for a company that sells sunscreen in the northeast United States.

On March 6, 2007, the Associated Press reported that Ed Nabors had won half of a $390 million jackpot, the largest lottery prize in US history at the time. Suppose he was given the choice of receiving his $195 million share paid out continuously over 20 years or one lump sum of $120 million paid immediately. (a) Which option is better if the interest rate is 6%, compounded continuously? An interest rate of 3%? (b) If Mr. Nabors chose the lump-sum option, what assumption was he making about interest rates?

(a) A bank account earns 10% interest compounded continuously. At what (constant, continuous) rate must a parent deposit money into such an account in order to save $100,000 in 10 years for a childs college expenses? (b) If the parent decides instead to deposit a lump sum now in order to attain the goal of $100,000 in 10 years, how much must be deposited now?

(a) If you deposit money continuously at a constant rate of $1000 per year into a bank account that earns 5% interest, how many years will it take for the balance to reach $10,000? (b) How many years would it take if the account had $2000 in it initially?

A business associate who owes you $3000 offers to pay you $2800 now, or else pay you three yearly installments of $1000 each, with the first installment paid now. If you use only financial reasons to make your decision, which option should you choose? Justify your answer, assuming a 6% interest rate per year, compounded continuously.

In Problems 2427 find the continuous interest rate that yields a future value of $18,000 in 20 years for each $9000 investment. A single $9000 deposit.

In Problems 2427 find the continuous interest rate that yields a future value of $18,000 in 20 years for each $9000 investment. An initial $6000 deposit plus a second $3000 deposit made three years after the first.

In Problems 2427 find the continuous interest rate that yields a future value of $18,000 in 20 years for each $9000 investment. An initial $3000 deposit plus a second $6000 deposit made three years after the first.

In Problems 2427 find the continuous interest rate that yields a future value of $18,000 in 20 years for each $9000 investment. An income stream of $300 per year.

A family wants to save for college tuition for their daughter. What continuous yearly interest rate r% is needed in their savings account if their deposits of $4800 per year are to grow to $100,000 in 15 years? Assume that they make deposits continuously throughout the year.

Big Tree McGee is negotiating his rookie contract with a professional basketball team. They have agreed to a three-year deal which will pay Big Tree a fixed amount at the end of each of the three years, plus a signing bonus at the beginning of his first year. They are still haggling about the amounts and Big Tree must decide between a big signing bonus and fixed payments per year, or a smaller bonus with payments increasing each year. The two options are summarized in the table. All values are payments in millions of dollars. (a) Big Tree decides to invest all income in stock funds which he expects to grow at a rate of 10% per year, compounded continuously. He would like to choose the contract option which gives him the greater future value at the end of the three years when the last payment is made. Which option should he choose? (b) Calculate the present value of each contract offer.

Sales of Version 6.0 of a computer software package start out high and decrease exponentially. At time t, in years, the sales are s(t) = 50et thousands of dollars per year. After two years, Version 7.0 of the software is released and replaces Version 6.0. Assuming that all income from software sales is immediately invested in government bonds which pay interest at a 6% rate compounded continuously, calculate the total value of sales of Version 6.0 over the two-year period.

The value of good wine increases with age. Thus, if you are a wine dealer, you have the problem of deciding whether to sell your wine now, at a price of $P a bottle, or to sell it later at a higher price. Suppose you know that the amount a wine-drinker is willing to pay for a bottle of this wine t years from now is $P(1 + 20t). Assuming continuous compounding and a prevailing interest rate of 5% per year, when is the best time to sell your wine?

An oil company discovered an oil reserve of 100 million barrels. For time t > 0, in years, the companys extraction plan is a linear declining function of time as follows: q(t) = a bt, where q(t) is the rate of extraction of oil in millions of barrels per year at time t and b = 0.1 and a = 10. (a) How long does it take to exhaust the entire reserve? (b) The oil price is a constant $20 per barrel, the extraction cost per barrel is a constant $10, and the market interest rate is 10% per year, compounded continuously. What is the present value of the companys profit?

You are manufacturing a particular item. After t years, the rate at which you earn a profit on the item is(20.1t) thousand dollars per year. (A negative profit represents a loss.) Interest is 10%, compounded continuously, (a) Write a Riemann sum approximating the present value of the total profit earned up to a time M years in the future. (b) Write an integral representing the present value in part (a). (You need not evaluate this integral.) (c) For what M is the present value of the stream of profits on this item maximized? What is the present value of the total profit earned up to that time?

In 1980, before the unification of Germany in 1990 and the introduction of the Euro, West Germany made a loan of 20 billion Deutsche Marks to the Soviet Union, to be used for the construction of a natural gas pipeline connecting Siberia to Western Russia, and continuing to West Germany (UrengoiUschgorodBerlin). Assume that the deal was as follows: In 1985, upon completion of the pipeline, the Soviet Union would deliver natural gas to West Germany, at a constant rate, for all future times. Assuming a constant price of natural gas of 0.10 Deutsche Mark per cubic meter, and assuming West Germany expects 10% annual interest on its investment (compounded continuously), at what rate does the Soviet Union have to deliver the gas, in billions of cubic meters per year? Keep in mind that delivery of gas could not begin until the pipeline was completed. Thus, West Germany received no return on its investment until after five years had passed. (Note: A more complex deal of this type was actually made between the two countries.)

In May 1991, Car and Driver described a Jaguar that sold for $980,000. At that price only 50 have been sold. It is estimated that 350 could have been sold if the price had been $560,000. Assuming that the demand curve is a straight line, and that $560,000 and 350 are the equilibrium price and quantity, find the consumer surplus at the equilibrium price.

Using Riemann sums, explain the economic significance of - q 0 S(q) dq to the producers.

Using Riemann sums, give an interpretation of producer surplus, - q 0 (p S(q)) dq analogous to the interpretation of consumer surplus.

In Figure 8.85, page 463, mark the regions representing the following quantities and explain their economic meaning: (a) pq (b) , q 0 D(q) dq (c) , q 0 S(q) dq (d) , q 0 D(q) dq p q (e) pq , q 0 S(q) dq (f) , q 0 (D(q)S(q)) dq

The dairy industry is an example of cartel pricing: the government has set milk prices artificially high. On a supply and demand graph, label p+, a price above the equilibrium price. Using the graph, describe the effect of forcing the price up to p+ on: (a) The consumer surplus. (b) The producer surplus. (c) The total gains from trade (Consumer surplus + Producer surplus).

Rent controls on apartments are an example of price controls on a commodity. They keep the price artificially low (below the equilibrium price). Sketch a graph of supply and demand curves, and label on it a price p below the equilibrium price. What effect does forcing the price down to p have on: (a) The producer surplus? (b) The consumer surplus? (c) The total gains from trade (Consumer surplus + Producer surplus)?

In Problems 4144, explain what is wrong with the statement. The future value of an income stream of $2000 per year after 10 years is $15,000, assuming a 3% continuous interest rate per year.

In Problems 4144, explain what is wrong with the statement. The present value of a lump-sum payment S dollars one year from now is greater with an annual interest rate of 4% than with an annual interest rate of 3%.

In Problems 4144, explain what is wrong with the statement. Payments are made at a constant rate of P dollars per year over a two-year period. The present value of these payments is 2P e2r, where r is the continuous interest rate per year.

In Problems 4144, explain what is wrong with the statement. Producer surplus is measured in the same units as the quantity, q.

In Problems 4548, give an example of: Supply and demand curves where producer surplus is smaller than consumer surplus.

In Problems 4548, give an example of: A continuous interest rate such that a $10,000 payment in 10 years time has a present value of less than $5000.

In Problems 4548, give an example of: An interest rate, compounded annually, and a present value that correspond to a future value of $5000 one year from now.

In Problems 4548, give an example of: An interest rate, compounded annually, and a table of values that shows how much money you would have to put down in a single deposit t years from now, at t = 0, 1, 2, 3, or 4, if you want to have $10,000 ten years from now (ignoring inflation).