P5-3Future value You have $100 to invest. If you put the money into an account

earning 5% interest compounded annually, how much money will you have in

10 years? How much money will you have in 10 years if the account pays 5% simple interest?

Personal Finance Problem

P5-5 Time value You have $1,500 to invest today at 7% interest compounded annually.

a. Find how much you will have accumulated in the account after (1) 3 years, (2) 6

years, and (3) 9 years.

b. Use your findings in part a to calculate the amount of interest earned in (1) the

first 3 years (years 1 to 3), (2) the second 3 years (years 4 to 6), and (3) the third

3 years (years 7 to 9).

c. Compare and contrast your findings in part b. Explain why the amount of interest

earned increases in each succeeding 3-year period.

P5-12 Present value concept Answer each of the following questions.

a. How much money would you have to invest today to accumulate $6,000 after

6 years if the rate of return on your investment is 12%?

b. What is the present value of $6,000 that you will receive after 6 years if the discount

rate is 12%?

c. What is the most you would spend today for an investment that will pay $6,000

in 6 years if your opportunity cost is 12%?

d. Compare, contrast, and discuss your findings in parts a through c.

Personal Finance Problem

LG 2 P5-13 Time value Jim Nance has been offered an investment that will pay him $500 three

years from today.

a. If his opportunity cost is 7% compounded annually, what value should he place

on this opportunity today?

b. What is the most he should pay to purchase this investment today?

c. If Jim can purchase this investment for less than the amount calculated in part a,

what does that imply about the rate of return he will earn on the investment?

P5-20 Present value of an annuity Consider the following cases

CaseAnnuity paymentInterest rate Annuity length (years

A $ 12,0007%3

B55,00012 15

C700 20 9

D140,000 5 7

E22,50010 5

MyLab

a. Calculate the present value of the annuity, assuming that it is

(1) An ordinary annuity.

(2) An annuity due.

b. Compare your findings in parts a(1) and a(2). All else being identical, which type

of annuityordinary or annuity dueis preferable? Explain why.

Personal Finance Problem

LG 2 P5-24 Funding your retirement Emily Jacob is 45 years old and has saved nothing for retirement.

Fortunately, she just inherited $75,000. Emily plans to put a large portion of

that money into an investment account earning an 11% return. She will let the money

accumulate for 20 years, when she will be ready to retire. She would like to deposit

enough money today so she could begin making withdrawals of $50,000 per year

starting at age 66 (21 years from now) and continuing for 24 additional years, when

she will make her last withdrawal at age 90. Whatever remains from her inheritance,

Emily will spend on a shopping spree. Emily will continue to earn 11% on money in

her investment account during her retirement years, and she wants the balance in her

retirement account to be $0 after her withdrawal on her ninetieth birthday.

a. How much money must Emily set aside now to achieve that goal? It may be helpful

to construct a timeline to visualize the details of this problem.

b. Emily realizes that once she retires she will want to have less risky investments

that will earn a slightly lower rate of return, 8% rather than 11%. If Emily can

earn 11% on her investments from now until age 65, but she earns just 8% on

her investments from age 65 to 90, how much money does she need to set aside

today to achieve her goal?

c. Suppose Emily puts all of the $75,000 that she inherited into the account earning

11%. As in part b, she will earn only an 8% return on her investments after age

65. If Emily withdraws $50,000 as planned on each birthday from age 66 to age

90, how much will be left in her account for her heirs after her last withdrawal?

P5-30 Value of a mixed stream For each of the mixed streams of cash flows shown in the

following table, determine the future value at the end of the final year if deposits are

made into an account paying annual interest of 12%, assuming that no withdrawals

are made during the period and that the deposits are made

a. At the end of each year (i.e., the first deposit occurs 1 year from now)

b. At the beginning of each year (i.e., the first deposit occurs immediately)

X

MyLab

Cash flow stream

YearABC

1$ 900$30,000$1,200

21,00025,0001,200

31,20020,000 1,000

410,0001,900

55,000

P5-36 Relationship between future value and present value: Mixed stream Using the information

in the accompanying table, answer the questions that follow.

XYearCash flow

0$ 0

1800

2900

31,000

4 1,500

52,000

a. Determine the present value of the mixed stream of cash flows, using a 5% discount rate.

b. Suppose you had a lump sum equal to your answer in part a on hand today. If

you invested this sum for 5 years and earned a 5% return each year, how much

would you have after 5 years?

c. Determine the future value 5 years from now of the mixed stream, using a 5%

interest rate. Compare your answer here to your answers in part b.

d. How much would you be willing to pay for this stream, assuming that you can at

best earn 5% on your investments?

P5-43 Deposits to accumulate future sums For each case shown in the following table,

determine the amount of the equal, end-of-year deposits necessary to accumulate

the given sum at the end of the specified period, assuming the stated annual

interest rate.

X

CaseSum to be accumulateAccumulation period (years)Interest rate

A$ 5,0003 12%

B100,000 20 7

C30,000 8 10

D 15,000 12 8

Personal Finance Problem

LG 6 P5-48 Loan amortization schedule Joan Messineo borrowed $45,000 at a 4% annual rate

of interest that she must repay over 3 years. The loan is amortized into three equal,

end-of-year payments.

a. Calculate the end-of-year loan payment.

b. Prepare a loan amortization schedule showing the interest and principal breakdown

of each of the three loan payments.

c. Explain why the interest portion of each payment declines with the passage of time.

While i am working on all these, i want to be able to make sure i did it right