Different cash flow.Given the following cash inflow at the end of each year,

LOADING...

,

what is the future value of this cash flow at

5 %

,

10 %

,

and

15

%

interest rates at the end of year 7?

What is the future value of this cash flow at

5

%

interest rate at the end of year 7?

Future

value.

A speculator has purchased land along the southern Oregon coast. He has taken a loan with the end-of-year payments of

$7 comma 800

for

11

years. The loan rate is

4

%.

At the end of

11

years, he believes that he can sell the land for

$110 comma 000

.

If he is correct on the future price, did he make a wise investment?

What is the future value of the loan

11

years from now?

$nothing

(Round to the nearest cent.)

P4-4 (similar to)

Future

value.

Jack and Jill are saving for a rainy day and decide to put

$70

away in their local bank every year for the next

20

years. The local Up-the-Hill Bank will pay them

6

%

on their account.

a.If Jack and Jill put the money in the account faithfully at the end of every year, how much will they have in it at the end of

20

years?

b. Unfortunately, Jack had an accident in which he sustained head injuries after only

10

years of savings. The medical bill has come to

$800

.

Is there enough in the rainy-day fund to cover it?

a. If Jack and Jill put the money in the account faithfully at the end of every year, how much will they have in it at the end of

20

years?

$nothing

(Round to the nearest cent.)

Future value. You are a new employee with the Metro Daily

Planet.

The Planet offers three different retirement plans. Plan 1 starts the first day of work and puts

$1 comma 400

away in your retirement account at the end of every year for

40

years. Plan 2 starts after 10 years and puts away

$2 comma 900

every year for

30

years. Plan 3 starts after 20 years and puts away

$ 4 comma 400

every year for the last

20

years of employment. All three plans guarantee an annual growth rate of

9

%.

a.Which plan should you choose if you plan to work at the Planet for

40

years?

b. Which plan should you choose if you plan to work at the Planet for only the next

30

years?

c. Which plan should you choose if you plan to work at the Planet for only the next

20

years?

d. Which plan should you choose if you plan to work at the Planet for only the next

10

years?

e. What do the answers in parts (a) through (d) imply about savings?

a.Which plan should you choose if you plan to work at the Planet for

40

years?(Select the best response.)

A.

Plan 1

because it offers the highest future value.

B.

Plan 2

because it offers the highest future value.

C.

Plan 3

because it offers the highest future value.

D.

Any one of the three plans because they offer the same future value.

Present

value.

A smooth-talking used-car salesman who smiles considerably is offering you a great deal on a "pre-owned" car. He says, "For only

8

annual payments of

$2 comma 700

,

this beautiful 1998 Honda Civic can be yours." If you can borrow money at

7

%,

what is the price of this car? Assume the payment is made at the end of each year.

If you can borrow money at

7

%,

what is the price of this car?

$nothing

(Round to the nearest cent.)

Annuity

due.

Reginald is about to lease an apartment for

30

months. The landlord wants him to make the lease payments at the start of the month. The monthly payments are

$1 comma 000

per month. The landlord says he will allow Reg to prepay the rent for the entire lease with a discount. The one-time payment due at the beginning of the lease is

$26 comma 790

.

What is the implied monthly discount rate for the rent? If Reg is earning

1.3

%

on his savings monthly, should he pay by month or make the one-time payment?

What is the implied monthly discount rate for the rent?

nothing

%

(Round to two decimal places.)

Perpetuities.

The Canadian Government has once again decided to issue a consol (a bond with a never-ending interest payment and no maturity date). The bond will pay

$50

in interest each year (at the end of the year), but it will never return the principal. The current discount rate for Canadian government bonds is

8.5

%.

What should this consol bond sell for in the market? What if the interest rate should fall to

7.5

%?

Rise to

9.5

%?

Why does the price go up when interest rates fall? Why does the price go down when interest rates rise?

If the current discount rate for Canadian government bonds is

8.5

%,

what should this bond sell for in the market?

$nothing

(Round to the nearest cent.)

Discount loan (interest and principal at maturity).Chuck Ponzi has talked an elderly woman into loaning him

$45 comma 000

for a new business venture. She has, however, successfully passed a finance class and requires Chuck to sign a binding contract on repayment of the

$45 comma 000

with an annual interest rate of

10

%

over the next

10

years. Determine the cash flow to the woman under a discount loan, in which Ponzi will have a lump-sum payment at the end of the contract.

What is the amount of payment that the woman will receive at the end of years 1 through

9

?

$nothing

(Round to the nearest cent.)

Interest-only loan (regular interest payments each year and principal at maturity).Chuck Ponzi has talked an elderly woman into loaning him

$35 comma 000

for a new business venture. She has, however, successfully passed a finance class and requires Chuck to sign a binding contract on repayment of the

$35 comma 000

with an annual interest rate of

9

%

over the next

15

years. Determine the cash flow to the woman under an interest-only loan, in which Ponzi will pay the annual interest expense each year and pay the principal back at the end of the contract.

What is the amount of payment that the woman will receive at the end of years 1 through

14

?

$nothing

(Round to the nearest dollar.)

Fully amortized loan (annual payments for principal and interest with the same amount each year). Chuck Ponzi has talked an elderly woman into loaning him

$20 comma 000

for a new business venture. She has, however, successfully passed a finance class and requires Chuck to sign a binding contract on repayment of the

$20 comma 000

with an annual interest rate of

6

%

over the next

10

years. Determine the cash flow to the woman under a fully amortized loan, in which Ponzi will make equal annual payments at the end of each year so that the final payment will completely retire the original

$20 comma 000

loan.

What is the amount of payment that the woman will receive at the end of years 1 through

10

?

$nothing

(Round to the nearest cent.)

Amortization schedule.Chuck Ponzi has talked an elderly woman into loaning him

$25 comma 000

for a new business venture. She has, however, successfully passed a finance class and requires Chuck to sign a binding contract on repayment of the

$ 25 comma 000

with an annual interest rate of

10

%

over the next

5

years. Ponzi may choose to pay off the loan early if interest rates change during the next

5

years. Determine the ending balance of the loan each year under the three different payment plans:

a. the discount loan

b. the interest-only loan

c. the fully amortized loan.

a.If Chuck chooses the discount loan, what is the ending balance of the discount loan in year 1?

$nothing

(Round to the nearest cent.)

Amortization.Loan Consolidated Incorporated (LCI) is offering a special one-time package to reduce Custom Autos' outstanding bills to one easy-to-handle payment plan. LCI will pay off the current outstanding bills of

$234 comma 000

for Custom Autos if Custom Autos will make an annual payment to LCI at an interest rtae of

10

%

over the next

5

years.

a.What are the annual payments of the loan?

b.What is the amortization schedule for this loan if Custom Autos wants to pay off the loan before the loan maturity in

5

years?

c.When will the balance be half paid off?

d.What is the total interest expense on the loan over the

5

years?

a. What is the annual payment of the loan?

$nothing

(Round to the nearest cent.)

Lottery.

Your dreams of becoming rich have just come true. You have won the State of Tranquility's Lottery. The State offers you two payment plans for the

$5 comma 000 comma 000

advertised jackpot. You can take annual payments of

$125 comma 000

at the end of the year for the next

40

years or

$1 comma 344 comma 670

today.

a.If your investment rate over the next

40

years is

11

%,

which payoff will you choose?

b. If your investment rate over the next

40

years is

7

%,

which payoff will you choose?

c. At what investment rate will the annuity stream of

$125 comma 000

be the same as the lump-sum payment of

$1 comma 344 comma 670

?

a.If your investment rate over the next

40

years is

11

%,

what is the present value of the

$125 comma 000

annual payments today?

$nothing

(Round to the nearest dollar.)

Challenge

problem.

Each holiday season, Michael received a U.S. savings bond from his grandmother. Michael eventually received twelve savings bonds as shown in the following table:

LOADING...

. The bonds vary in their rates of interest and their face values. Assume today is December 31, 2011. What is the value of this portfolio of U.S. savings bonds? On what date does each of the individual bonds reach its face value or maturity date (note that the price is half the face value)? Estimate to the nearest month and year for each bond.Note: The bonds continue earning interest past their maturity dates.

What is the current value of the bond that was issued on

12 divided by 31 divided by 1990

?

$nothing

(Round to the nearest cent.)