Problem Set 1
FINA1310, Fall 2021
Professor Alexandr Kopytov
Due on October 3, 22:00 HK time. Each group should submit one copy only. No late
submission will be accepted. Submissions should be done either electronically via Moodle
link or physically to FINA1310ABC mailbox at 9/F, KKL Building.
Do not forget to
indicate your name, UID, group number. Before submission, you are suggested to make a
copy of your work for future reference.
1. (20 points) Suppose that you are going to graduate in one year and get a job that will pay you
$500,000 every year. You are planning to save 20% of your annual income every year, starting from
next year. Current interest rate is 4%.
(a) (7 points) How many years will it take it for you to become a millionaire, that is, have at least
$1,000,000 in your savings account?
(b) (3 points) Suppose now that you really want to become a millionaire by the end of year 5.
What should be the interest rate for you to be able to achieve this goal?
(c) (10 points) Suppose now that your annual income will grow at 5% rate every year. That is,
your salary will be $500,000 in year 1, $525,000 in year 2, $551,250 in year 3, and so on. If you
save 20% of your annual income for 10 years, how much money will you accumulate on your
saving account by the end of year 10? Suppose that interest rate is 4%.
2. (25 points) A potential employer offers you two five-year contracts. The first implies monthly salary
of $5,000, with the first salary coming at the end of the first month. The second one implies a
one-time payment of $350,000 at the end of the contract. Current annual rate (APR) is 6% (assume
monthly compounding throughout the problem).
(a) (10 points) Which contract do you choose? Why?
(b) (5 points) What monthly salary will make you exactly indifferent between the first and the
second contracts?
(c) (5 points) Suppose that the interest rate is 8% instead. Will your decision change? Why does
the level of interest rate affect your decision?
(d) (5 points) Suppose again that the interest rate is 6%. Suppose that a potential employer
modifies the first contract by paying you upfront each month. That is, if you take this contract,
your first payment will come immediately. Will your decision change?
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3. (15 points) A corporation XYZ issued a preferred stock that promises to pay $5 dividend each
quarter for the next 10 years (the first payment is going to arrive in one quarter). After that, the
dividends will be permanently increased to $7 per quarter. An effective annual rate is 7.99%.
(a) (5 points) What is a correct interest rate you need to use to discount dividends?
(b) (10 points) What should be the the price of such a stock?
4. (15 points) Today is December 31 of 2021, and you are considering to buy an annuity. Its current
market price is $1,000. It pays semiannually for 10 years, on January 1 and July 1 of each year. Its
first payment is going to come tomorrow. Annual percentage rate is 6%.
(a) (5 points) What is annual payment of this annuity?
(b) (5 points) How much will you be willing to pay for this annuity on December 31 of 2024?
(c) (5 points) How much will you be willing to pay for this annuity on December 1 of 2021?
5. (25 points) Suppose that your friend is 25 years old and starting her career. Her salary is going to
be $100,000. She is planning to retire at the age of 65 and wants her retirement payments to cover
20 years. Interest rate is 5%.
(a) (5 points) Suppose that your friend wants to receive $70,000 every year for 20 years after her
retirement. How much money should her retirement account have at the moment of her retirement? Suppose that the first payment will come one year after the moment of her retirement.
(b) (7 points) Suppose that your friend wants to save a constant fraction of her annual income.
What is this fraction if she wants to reach her goal of part (a)?
(c) (7 points) How does your answer to part (b) change if your friend’s salary is expected to grow
at 2% per year (that is, her first salary is $100,000, her second salary is $102,000, and so on)?
(d) (6 points) Suppose again that your friend’s salary is $100,000 and does not change over time.
However, suppose now that at the age of 30 she expects to inherit $150,000 and wants to put
half of this sum in her retirement account. How does your answer to part (b) change?
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