2) Assume, today is January 1, 2023 and you have 180000 KZT on hand now. You can deposit your money to bank that pays interest at an annual rate of 12%. How much money will you have as of January 1, 2024? (Hint: Draw the cash flow time line properly and solve by means of as many ways as you can)

3) Assume, today is January 1, 2023. You will need 1500000 KZT to start your own business right after your graduation two years later. You are planning to deposit some amount of money to a savings account today that pays at an annual rate of 8%. How large must your deposit must be today, so that after 2 years you will have the required 1500000 KZT. (Hint: Draw the cash flow time line properly and solve by means of as many ways as you can)

4) For the questions #2 and #3 find the solution when we use the following compounding periods: a. Interest is compounded semiannually (also calculate the effective annual rate)

b. Interest is compounded quarterly (also calculate the effective annual rate) 5) Assume today is March 1, 2023 and you will deposit 350000 KZT to savings account that pays interest at an annual rate of 16%. To the closest year, how long will it take your deposit to grow to 990000 KZT. (Hint: Draw the cash flow time line properly and solve by means of as many ways as you can)

6) Assume today is August 31, 2023 and you will deposit 750000 KZT to a bank for 4 years. You will have 1058686.2 KZT on August 31, 2022. Calculate the interest rate on your deposit? (Hint: Draw the cash flow time line properly and solve by means of as many ways as you can)

7) For the questions #5 and #6 find the solution when we use the following compounding periods: a. Interest is compounded semiannually (also calculate the effective annual rate)

b. Interest is compounded quarterly (also calculate the effective annual rate) You will use ordinary annuities between questions 8-16

8) Assume, today is January 1, 2023. You are planning to deposit 200000 KZT every year starting from January 1, 2024 to finance your future business. Interest rate on your deposit will be 16% and last deposit will be on January 1, 2023. How much money will you have in your bank account as of January 1, 2023? (Hint: Draw the cash flow time line properly and solve by means of as many ways as you can)

9) Assume, today is January 1, 2023 and you would like to purchase a house for your family by getting a mortgage loan from a local bank. Annual interest rate on mortgage loans is 20%. You think that, you can pay 1000000 KZT at the end of every year for the following seven years. How will you borrow from the bank today?

(Hint: Draw the cash flow time line properly and solve by means of as many ways as you can)

10) An automobile loan carries annual interest rate of 9%. List price of the automobile is 3.5 million KZT. And you will make the payments at the end of every year for the following 7 years. How much will you pay every year? (Illustrate the solution on a cash flow time line)

11) You are planning to purchase a house on a mortgage loan. Sales price of the house is 9 million KZT. Market interest rate on similar real estate loans is 15% and annually you can pay 1.8 million KZT. To the closest year how long will it take to pay off all your loan? (Illustrate the solution on a cash flow time line) N

12) According to your calculations, you will need 15 million KZT to start your new business. After many days of research, you decided to get a mortgage loan form a national bank. You will get the loan for 10 years and you will be capable of paying 2235442 KZT annually. To the closest value, calculate the interest rate on the loan. I

13) Assume today is January 1, 2023 and you will need 1300000 KZT as of January 1, 2023. How much must you deposit at the end of each year, so that you will have the required amount on January

20 1, 2023 when annual interest rate on deposits is 9%. (Hint: Draw the cash flow time line properly and solve by means of as many ways as you can)

14) Assume today is January 1, 2023 and you will deposit 200000 KZT at the end of each year for the following 5 years. If the annual interest rate on deposits is 13%, how much money will you have in your account as of January 1, 2023? (Hint: First payment will be on December 31, 2023 and total number of payments will be five and draw the cash flow time line properly and solve by means of as many ways as you can)

15) You are planning to start a local IT service company 4 years later. According to your calculations, you will exactly need 3200000 KZT. Currently you can save and deposit 660000 KZT annually. How much must the annual interest rate be, so that you will have 3200000 KZT et the end of the four year period? (Hint: If you cannot find the exact result, just indicate within an interval, such a x%< interest rate < y% ) (Hint: Draw the cash flow time line properly and solve by means of as many ways as you can)

16) If you start making deposits of 325000 KZT every year, starting from the next year, how long will it take your deposit to reach to 1877312 KZT when annual interest rate on deposits is 8%. (Hint: Draw the cash flow time line properly and solve by means of as many ways as you can)

17) Now rework on questions 8-16 assuming that all cash flows constitute annuities due.

18) You are to select one of the following alternatives. You will deposit 500000 KZT now and receive 890000 KZT after 6 years or you will deposit 500000 KZT now and receive 1050000 KZT after 9 years. Which one will you prefer? Why? (Hint: you have to calculate the interest rates of both alternatives)

19) Find the present value of the following cash flow streams when the interest rate is 14%, 18% and 24%. Explain why the present value of CF A is more sensitive than the present value of CFB .

Year

CFA

CFB

1

12000

22000

2

15000

19000

3

18000

16000

4

21000

13000

5

24000

10000

20) Assume you have three investment alternatives. Alternative1, offers 151000 KZT for the following ten years. Alternative 2, offers 191720 KZT for the following five years. Alternative 3 offers 291290 KZT for the following five years. Calculate the present value of the three alternatives assuming the discount rate is 8%, 14% and 22%. Plot your findings on a graph on which horizontal axis will indicate the different interest rates and vertical axis will indicate the present values of each cash flow. Which graph is steeper? Which graph is flatter? Try to reach a conclusion about the present value sensitivity of long, short and medium term investments based on your findings.

21) You are planning to purchase a flat in the center of the city. Sales price of the flat is 8 million KZT. As a new graduate, currently you have no personal savings, so you have to get a home 21 mortgage loan form a national bank. Interest rate on medium term mortgage loans is 16%. According to your calculations, you cant pay more than 2 million KZT to the bank in a year.

a) Calculate within how many years it will take you to pay off all your debt.

b) Prepare the amortization schedule.

22) Assume Bank A charges 11.71% (simple interest) on one year semiannual compounding mortgage loans. What should be the simple interest of Bank B that uses quarterly compounding, so that effective interest rate of both banks will be equal?

23) In 2007, GDP of Kazakhstan was 22.2 billion dollars. In 2022, GDP was 186.2 billion dollars. During ten years GDP of the country increased by approximately by 740%, which means average GDP increased by 74% every year. Is this statement true? If not, explain.