Chapter 7 Packet
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Chapter Topics/Suggested Reading
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Practice problems!!!
Review Questions
1. Simple vs compound interest
a. If you earn interest on only the principal, you earn ________________ interest. If
you earn interest on the principal and interest, you earn ________________
interest.
b. Time value of money assumes ________________ interest.
c. If you are paying interest, you should prefer ________________ interest and if you
are receiving interest, you should prefer ________________ interest
2. PV vs FV
a. The value of a future cash flow today is the ________________ while the value of a
cash flow in the future is the ________________.
b. Assuming a positive interest rate, the ________________ should be larger than the
________________
3. Moving a present value to a future value is called ________________ while moving a
future value to a present value is called ________________
4. A lump sum is best described as ________________________________ while an annuity is
best described as ________________________________________________
Chapter 7 Packet
Simple Interest Versus Compound Interest
1. You invest $100 at 5% simple interest for 3 years.
a. How much will you earn in interest in year 1 only? How much in total will
you have at the end of year 1?
b. How much will you earn in interest in year 2 only? How much in total will
you have at the end of year 2?
c. How much will you earn in interest in year 3 only? How much in total will
you have at the end of year 3?
2. Now you will invest $100 at 5% compound interest for 3 years.
a. How much will you earn in interest in year 1 only? How much in total will
you have at the end of year 1?
b. How much will you earn in interest in year 2 only? How much in total will
you have at the end of year 2?
c. How much will you earn in interest in year 3 only? How much in total will
you have at the end of year 3?
d. Can you write a one formula that would show how to get from your initial
investment of $100 to what you will have in total at the end of year 3?
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Chapter 7 Packet
PV And FV On A Timeline
1. What does finding a future
value of a cash flow look
like?
2. What does finding a present
value of a cash flow look like?
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Interpreting PV and FV
1. PV and FV
a. What is the PV of receiving $2,500 in 2 years assuming an 8% interest rate?
b. You would be willing to pay ________________ to receive ________________ in 2 years
and would effectively be earning a return of ________________.
c. You could invest ________________ for 2 years at a rate of ________________ and have
an ending balance of ________________.
2. PV and FV
a. What is the FV of investing $500 today for 5 years with a 6% interest rate?
b. You would be willing to pay ________________ to receive ________________ in 5 years
and would effectively be earning a return of ________________.
c. You could invest ________________ for 5 years at a rate of ________________ and have
an ending balance of ________________.
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Lump Sum Practice
1. You just invested $400,000 in an investment account that you expect to earn 8%
per year. If you withdraw the funds in 20 years to buy a house, how much can
you spend on your house?
2. You are offered the option to buy a security that offers a payment of $30,000 in 5
years. If you believe that funds can be invested currently for 6%, how much
should you pay for the security today?
3. You bought an asset for $10,000 and sold it for $20,000 after 10 years. What was
the annual rate of return on this investment?
4. An investor expects a stock to double in 7 years. What is the expected annual
rate of growth in the price of the stock?
5. You are offered two jobs. One initially pays $45,000 annually, and your salary
will grow annually at 10%. The other pays $42,000 annually, but your salary will
grow at 12%. After 10 years, which job pays the higher salary?
6. The Big-Sox currently have 30,000 spectators per game and anticipate annual
growth in attendance of 9%. If the Big Stadium holds 65,000 people, how long
will it take for the team reach capacity?
7. You bought a Picasso for $50,000 and sold it after 5 years for $88,000. What was
the annual return on the investment?
8. AZ's dividend rose from $1 to $1.61 in five years. What has the dividend's annual
rate of growth?
9. If a company paid a dividend of $1 in 2012 and the dividend grows annually by 7
percent, what will be the dividend in 2017?
10. How much additional interest will you earn on $1,000 at 10 percent for 10 years
if interest is compounded semi-annually instead of annually?
Chapter 7 Packet
Annuities On A Timeline
1. What does an
annuity look like?
2. What does finding a future
value of an annuity look
like?
3. What does finding a
present value of an
annuity look like?
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Interpreting PV and FV
1. PV and FV
a. How much do I need to deposit annually to have an account with $500,000 in
8 years? Assume the account will earn 5%.
b. I will deposit a total of ________________ which is ________________ than $500,000
because every deposit I make will earn ________________.
2. PV and FV
a. Your account currently has a total of $40,000 in it. If you expect the account
to earn 8% a year, how many withdrawals of $5,000 can you make?
b. I have ________________ today but can withdraw ________________a year for
________________ years for a total amount of ________________ because I am earning
________________ interest.
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Annuity Practice
1. An investment is expected to generate $1,000,000 each year for 4 years. If the
firm's cost of funds is 10%, what is the maximum amount the firm should pay for
the investment?
2. A person has an individual retirement account and can deposit $2,000 a year.
What will be the account balance after 8 years if the account earns 5% per year?
3. An annuity offers $1,000 for 10 years. If you can earn 12% annually on your
funds, what is the maximum amount you should pay for this annuity?
4. If a freshman wants to buy a car at graduation that costs $25,000, how much
must be saved annually if the funds earn 5%?
5. If an individual can save $1,500 annually, how much will have been accumulated
after 4 years if the funds earn 7%?
6. Your account currently has $50,000 in it. You would like to withdraw $8,000 a
year. If your account earns 7%, how many years can you make withdrawals?
7. You borrow $100,000 to buy a house; if the annual interest rate is 6% and the
term of the loan is 20 years, what is the annual payment required to retire the
mortgage loan?
8. You bought a stock for $30 and after 10 years sold it for $50. It paid an annual
dividend of $2. What was your annual return? (Hard)
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Extra Practice
1. You are given the opportunity to purchase an investment that would promise to give
you $5,000 in 6 years. If you think that this investment should be earning at least 12%,
how much are you willing to pay for the investment today?
2. You decide you want your child to be a millionaire. You have a son today and you
deposit $15,000 in an investment account that earns 9% per year. The money in the
account will be distributed to your son whenever the total reaches $1,000,000. How old
will your son be when he gets the money?
3. Eight years ago, your account had a balance of $4,000 in it and now has a balance of
$7,000. What rate of return did you earn on this account?
4. You borrow $25,000 to buy a car and agree to make 4 annual payments of $9,000 repay
the loan. What annual rate of interest are you being charged?
5. You would like to have $5,000 to buy a scooter. You can only afford to save $1,000 a
year. If your savings account earns 5%, how long will it take before you can purchase
your scooter?
6. You charged $3,000 on your credit card during spring break. Your credit card company
charges you 22% annual interest. If you make annual payments of $800, how long will it
take to pay off your balance?
7. At an interest rate of 10%, how long will it take to triple your money?
8. Your daughter is born today and you want her to be a millionaire by the time she is 35
years old. You open an investment account that promises to pay 12% per year. How
much money must you deposit each year, so your daughter will have $1,000,000 by her
35th birthday?
9. How much money will you have if you place $400 into a savings account earning 8% if
you allow the money to grow for 2 years?
10. Jimmy just bought a new Ford SUV for his business. To purchase the vehicle Jimmy took
out an amortized loan for $40,000. The car dealership made the loan at 10% interest for
five years. Determine the amount of Jimmy's annual payment.
11. You borrowed $250,000 to build a home by taking out a 30 year loan that has an
interest rate of 8%. What will your annual payments be?
12. You originally had $500 in an account that has been earning an annual interest rate of
8%. The balance is now $1,400. How many years has the money been growing?
13. How much would you be willing to pay for a 10-year annuity if the payments are
$20,000 per year and you want to earn a rate of return equal to 4% per year?
14. You would like to buy a $20,000 boat in 6 years. How much should you invest today if
you expect to earn 8% a year?
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15. You have been accepted to study gourmet cooking at a school in Paris. You will need
$10,000 every year for the next three years to cover tuition and living expenses. Mom
and Dad have agreed to pay for your education, and want to make one deposit today in a
bank account earning 6% interest. How much must they deposit now so that you can
withdraw $10,000 each year for the next 3 years?
16. Ann deposited $1,000 in a bank account, and 10 years later she closes out the account,
which is worth $2,000. What annual rate of interest has she earned?
17. A financial analyst tells you that investing in stocks will allow you to double your money
in 7 years. What annual rate of return is the analyst assuming you can earn?
18. You just graduated and landed your first job. You know that you should begin the job of
saving for retirement as soon as possible, so you decided to put away $2,000 at the end
of each year in a Roth IRA. Your expected annual rate of return on the IRA is 7%. How
much will you accumulate at retirement after 40 years of investing?
19. Bowflex’s television ads say you can get a Treadclimber that sells for $8,000 for 4
annual payments of $2,500. What annual rate of interest are you paying on this loan?
20. Bill borrowed $100,000 today that he must repay in 15 annual end-of-year installments
of $10,000. What annual interest rate is Bill paying on his loan?
21. You currently have $100,000 in an account that has been earning 8% a year. You would
like to not work for as long as possible. You will need to withdraw $40,000 a year for
living expenses and will go back to work once the account balance reaches $10,000.
How long can you not work for? (HARD)
22. Your savings account currently has $250,000. You would like to withdraw $30,000 a
year for the next 7 years to cover living expenses while you endure a PhD program. If
the account is expected to earn an annual rate of 10%, how much will you have left in
your account once you finish the program? (HARD)
23. You opened a savings account 5 years ago with $100. Today the account has $30,000 in
it. You have made annual payments of $3,000 each year. What annual interest rate have
you earned on the past 5 years? (HARD)
24. You are opening a savings account today by depositing $10,000 today and then plan on
depositing an additional $2,000 every year. How many deposits will you have to make
before the account balance reaches $50,000 if the account earns 6% a year? (HARD)
25. You currently have $40,000 in a savings account that earns 12% interest. You would like
to make annual withdrawals of $5,000. You would also like the account balance to not
fall below $10,000. How many withdrawals can you make? (HARD)
26. You currently have a savings account with a balance of $100,000. You would like to
withdraw a constant amount for the next 40 years, but you would also like to have a
balance left in the account of $20,000. The account is expected to earn 6% per year. How
much can you withdraw every year? (HARD)