Iufm _ Lecture 2 _ Homework Handout.docx

FUNDAMENTALS OF FINANCIAL MANAGEMENT
TUTORIAL – Lecture 2
1. Textbook, Chapter 5: 5, 8, 11, 15, 20, 22, 28, 29, 36, 39, 41, 43, 56, 62, 72
5. Future Values. You deposit $1,000 in your bank account. (LO5-1)
a. If the bank pays 4% simple interest, how much will you accumulate in your account after 10 years?
b. How much will you accumulate if the bank pays compound interest?
a. Simple interest: FV =PV ( 1+ ( r∗n ) )=1,000∗( 1+ ( 4 %∗10 ) )=$ 1,400
b. Compound interest: FV =PV ∗( 1+r )n=1,000∗ (1+ 4 % )10 =$ 1,480.24
8. Future Values. How long will it take for $400 to grow to $1,000 at the following interest rates?
(LO5-1)
a. 4%

PV =
c. 8%

PV =

FV n

( 1+ r )

FV n

( 1+ r )

c. 16%

PV =

n

n

→ 400=

→ 400=

FV n

( 1+ r )

n

1, 000
n
n
→(1. 04) =2.5 → log (1. 04) =log ( 2.5 ) → n=23.36
n
( 1+ 4 % )

1 , 000
→(1.08)n=2.5 → log (1.08)n=log ( 2.5 ) → n=11.9 1
n
( 1+8 % )

→ 4 00=

1, 000
n
n
→(1.16) =2.5 → log (1. 16) =log ( 2.5 ) → n=6.17

n
( 1+ 16 % )

11. Present Values. You can buy property today for $3 million and sell it in 5 years for $4 million.
(You earn no rental income on the property.) (LO5-2)
a. If the interest rate is 8%, what is the present value of the sales price?

PV =

FV n

( 1+ r )

n

→

4 , 000,000
=$ 2,722,332.79
( 1+ 8 % )5

b. Is the property investment attractive to you?
No, The sale value of property in the future is $4,000,000 and the present value of the future cash
flows is $2,722,332.79 which is a complete loss for the organization as the investment itself is
$3,000,000.
c. Would your answer to part (b) change if you also could earn $200,000 per-year rent on the
property?
The rent is paid at the end of each year.
Rent
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15. Calculating the Interest Rate. Find the interest rate implied by the following combinations of
present and future values. (LO5-2)

20. Annuities. A famous quarterback just signed a $15 million contract providing $3 million a year for
5 years. A less famous receiver signed a $14 million 5-year contract providing $4 million now and $2
million a year for 5 years. The interest rate is 10%. Who is better paid? (LO5-3)

28. Annuities. You want to buy a new car, but you can make an initial payment of only $2,000 and can
afford monthly payments of at most $400. (LO5-3)
a. If the APR on auto loans is 12% and you finance the purchase over 48 months, what is the
maximum price you can pay for the car?
b. How much can you afford if you finance the purchase over 60 months?

29. Annuities. You can buy a car that is advertised for $24,000 on the following terms: (a) pay $24,000
and receive a $2,000 rebate from the manufacturer; (b) pay $500 a month for 4 years for total
payments of $24,000, implying zero percent financing. Which is the better deal if the interest rate is
1% per month? (LO5-3)

36. Annuity Due. A store offers two payment plans. Under the installment plan, you pay 25% down
and 25% of the purchase price in each of the next 3 years. If you pay the entire bill immediately, you
can take a 10% discount from the purchase price. (LO5-3)
a. Which is a better deal if you can borrow or lend funds at a 5% interest rate?
b. How will your answer change if the payments on the 4-year installment plan do not start for a full
year?

39. Amortizing Loan. You take out a 30-year $100,000 mortgage loan with an APR of 6% and monthly
payments. In 12 years you decide to sell your house and pay off the mortgage. What is the principal
balance on the loan? (LO5-3)

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41. Retirement Savings. A couple will retire in 50 years; they plan to spend about $30,000 a year in
retirement, which should last about 25 years. They believe that they can earn 8% interest on
retirement savings. (LO5-3)
a. If they make annual payments into a savings plan, how much will they need to save each year?
Assume the first payment comes in 1 year.
b. How would the answer to part (a) change if the couple also realize that in 20 years they will need to
spend $60,000 on their child’s college education?

43. Retirement Savings. You believe you will need to have saved $500,000 by the time you retire in 40
years in order to live comfortably. You also believe that you will inherit $100,000 in 10 years. If the
interest rate is 6% per year, how much must you save each year to meet your retirement goal? (LO53)

56. Effective Interest Rate. First National Bank pays 6.2% interest compounded semiannually. Second
National Bank pays 6% interest compounded monthly. Which bank offers the higher effective annual
interest rate? (LO5-4)
62. Effective Interest Rate. Suppose you can borrow money at 8.6% per year (APR) compounded
semiannually or 8.4% per year (APR) compounded monthly. Which is the better deal? (LO5-4)
72. Real versus Nominal Annuities. You plan to retire in 30 years and want to accumulate enough by
then to provide yourself with $30,000 a year for 15 years. (LO5-5)
a. If the interest rate is 10%, how much must you accumulate by the time you retire?

b. How much must you save each year until retirement in order to finance your retirement
consumption?
c. Now you remember that the annual inflation rate is 4%. If a loaf of bread costs $1 today, what will
it cost by the time you retire?
d. You really want to consume $30,000 a year in real dollars during retirement and wish to save an
equal real amount each year until then. What is the real amount of savings that you need to
accumulate by the time you retire?
e. Calculate the required preretirement real annual savings necessary to meet your consumption
goals. f. What is the nominal value of the amount you need to save during the first year? (Assume the
savings are put aside at the end of each year.)
g. What is the nominal value of the amount you need to save during the 30th year?

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2. A wealthy relative give Barney $5,000 to help provide for his newborn child’s university fee. He
decides to invest this money at 10% p.a. until his child is ready to go to university. How much will
be in the account 18 years from now?
0

18

PV

FV

FV n=PV (1+r )n= $5,000 * (1+10%)18 = $27,799.59

3. Barney wants to provide $20,000 for his newborn child’s education, which will begin 18 years
from today. How much should Barney invest now if interest rate is 10% p.a.?
0

18

PV

FV

PV =

FV n
n

(1+r )

=

$ 20,000
=$ 3,597.16
18
(1+10 %)

4. How long will it take for a $1,000 investment to double in size when invested at the rate of 8%
per year?

PV =

FV n

( 1+ r )

n

→ 1,000=

2,000
n
n
→(1.08) =2→ log ( 1.08) =log ( 2 ) → n=9.01
n
( 1+ 8 % )

5. Suppose you have $500 to invest and you want to know how long will it take for this amount to
double in size if the interest rate is 10% p.a.

PV =

FV n

( 1+ r )

n

→ 500=

1,000
→( 1.1)n=2 → log (1.1)n=log ( 2 ) →n=7.27
n

( 1+ 10 % )

6. You borrow money on your credit card at 17.5% p.a., compounding quarterly. What is the
effective annual interest rate?
7. The following interest rates are being offered by three competing banks: 4% compounded
monthly; 4.1% compounded quarterly; 4.15% compounded annually. Which one is the most
attractive?
8. Barney lends $100,000 to John, his cousin in 10 years at 5% p.a.
a. how much John have to pay after 10 years (if use simple interest rate)
b. how much John have to pay after 10 years (if use compounded interest rate)
c. assume that Barney lends $100,000 to John, using simple interest rate, but wants to
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receive the payment which is equal to that if using compounded interest. What should
the interest rate be?
9. You have just received a letter from your aunt, which advises that she has written you into her will.
On her passing, you will receive an inheritance of $50,000. Assuming r = 8% p.a., what’s the
inheritance worth in today’s dollars if your aunt lives another 5 years? 15 years?

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10. On a contract you have a choice of receiving $25,000 six years from now or $50,000 twelve years

from now. At what implied compound annual interest rate should you be indifferent between the
two contracts?
11. You have just won the prize in the State lottery. A recent innovation is to offer prize winners a
choice of payoffs. You must choose one of the following prizes:
a. $1,000,000 paid immediately
b. $ 600,000 paid exactly one year from today, and another $600,000 paid exactly 3 years from
today
c. $ 70,000 payment at the end of each year forever (first payment occurs exactly 1 year from today)
d. an immediate payment of $600,000, then beginning exactly 5 years from today, an annual
payment of $50,000 forever
e. an annual payment of $200,000 for the next 7 years (first payment occurs exactly 1 year from
today
f. Require: You believe that 8% p.a. compounded annually is an appropriate discount rate.
Assuming you wish to maximize your current wealth, which is the best prize?
12. Ann buys a new computer. The stated priced is $2,000, but the retailer has a special offer whereby
she have to pay $400 immediately and then another $400 each year of the next 7 years. If the
interest rate is 8% p.a., what is the effective cash price?
13. Mr. and Mrs. Haiku have two offers for their apartment in Tokyo. The first calls for payment of ¥50
million now and ¥50 million in one year. The second would pay ¥90 million immediately. The
appropriate interest rate is 4%. Which offer has the higher PV?
14. Muffin Megabucks is considering two different savings plans in 10 years. The first plan would have
her deposit $500 every six months, and she would receive interest at 7% p.a. (compounding semiannually). Under the second plan she could deposit $1,000 every year with the rate of interest of
7.5% p.a. (compounding annually).
Which plan should Muffin use? (Assuming that the initial deposit of Plan 1 would be made 6 months
from now, and with Plan 2, one year hence)
15. Kate’s financial advisor tells her that she will need $2 million to fund her retirement. She plans to
work for another 30 years before retiring. She will make 30 contributions to a pension plan. How
much will each contribution be, if the interest rate is 9% p.a.?
16. Mary has just retired and has $1 million in her retirement account. Her bank offers an arrangement
whereby the bank takes her $1 million now and pays her $110,000 at the end of each year for the

next 20 years. Is it a fair deal, if the offered rate is 10% p.a.?

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17. Joe Hernandez has inherited $25,000 and wishes to purchase an annuity that will provide him with a
steady income over the next 12 years. He has heard that the local bank is currently paying 6% p.a.
(compounding annually). If he were to deposit his fund, what is the equal amount would he be able
to withdraw at the end of each year for 12 years?
18. Your company anticipates the introduction of environmental protection laws 3 years from now.
Under these laws you will have to pay an environment tax of $5,000 at the end of each year. If the
rate is 6% p.a., what is the present value of your company’s obligation under this law?
(Note: the first payment will be four years from now)
19. Vernal Equinox wishes to borrow $10,000 for three years. A group of individuals agrees to lend him
this amount if he contracts to pay them $16,000 at the end of the three years. What is the implicit
compound annual interest rate implied by this contract?
20. The Happy Hang Glide Company is purchasing a building and has obtained a $190,000 mortgage loan
for 20 years. The loan bears a compound interest rate of 17% p.a. and calls for equal annual
installment payments at the end of each of 20 years. What is the amount of annual payment?

21. Your wealthy uncle established a $1,000 bank account for you when you were born. For the first 8
years of your life, the interest rate earned on the account was 6% p.a. Since then, rates has been
only 4% p.a. Now you are 21 years old and ready to cash in. How much is in your account?
22. Mary enters into a loan agreement to borrow $90,000 to help finance the purchase of her new home.
a. The agreement specifies the term of 20 years with monthly repayment at the fixed rate of 9%
p.a. (compounded monthly). What is her monthly payment?
b. Five years has passed. A rival lender offers to refinance Mary her loan at fixed rate of 8% p.a.

(compounded monthly). Cost associated with this refinancing is $1,500. Should her refinance?
c. Suppose 9 years have passed since Mary enters the original loan. She’s considering making an
extra payment of $10,000 off her loan. If she plans to keep the term of the loan the same, how
much will her monthly repayment reduce?

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