Financial Management 2019
TUTORIAL – Lecture 2
1. Textbook, Chapter 5: 5, 8, 11, 15, 20, 22, 28, 29, 36, 39, 41, 43, 56, 62, 72
2. A wealthy relative give Barney $5,000 to help provide for his new born 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?
3. Barney wants to provide $20,000 for his new born child’s education, which will begin 18 years from
today. How much should Barney invest now, if interest rate is 10% p.a.?
4. How long will it take for a $1,000 investment to double in size when invested at the rate of 8% per
year?
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.
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 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?
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?
Prepared by: Dr. Tien C. Nguyen
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Financial Management 2019
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 semi-annually).
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.?
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?
Prepared by: Dr. Tien C. Nguyen
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Financial Management 2019
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?
Prepared by: Dr. Tien C. Nguyen
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