FINANCE MATHEMATICS EXAMPLES

 All interest rates are annual percentage rate (APR) unless otherwise stated. Day count convention is 365 days unless otherwise stated.

1.   A person deposits 5,000 TL into a time deposit account. Maturity is 92 days, interest rate is 12 %.  What is the amount of interest received in 92 days?

 

2.   A person deposits 25,000 TL into a time deposit account and receives 740 TL interest. Interest rate is 9 %. What is the maturity in days?

 

3.   A person deposits 8,000 TL into a time deposit account and receives 105 TL interest. Maturity is 60 days. What is the interest rate?

 

4.   A person deposits 7,000 TL into a one-year time deposit account. Interest rate in the first year is 9 %. Expected interest rate in the second year is 12 %, expected interest rate in the third year is 14 %, expected interest rate in the fourth year is 10 %. What is the future value in four years compounded yearly?

 

5.   A person deposits 12,000 TL into a three-month time deposit account. Interest rate is 16 %. What is the future value in 3 years compounded every three-month.

 

7.   A person deposits 17,000 TL into a six-month time deposit account. Interest rate is 8 %. What is the future value in five years compounded every-six month?

 

8.   A person deposits 23,000 TL into a six-month time deposit account. Interest rate for the first six-month is 10 %. Expected interest rate for the second six-month is 12 %.  Expected interest rate for the third six-month is 15 %. Expected interest rate for the fourth six-month is 16 %.   Expected interest rate for the fifth six-month is 14 %.  Expected interest rate for the sixth six-month is 12 %.  Expected interest rate for the forth year is 10 %. What is the future value in four years compounded every-six month?

 

9.   A person deposits 5,000 TL into a one-month time deposit account. Interest rate is 9 %. What is the future value in three years compounded every-month.

 

10. What is the present value of 40,000 TL received in 7 years. Interest rate is 10 %.

 

11. A person needs 60,000 TL at the end of the fifth year. She wants to deposit her money into a three-month time deposit account. How much money does she have to deposit today so that she receives 60,000 TL at the end of the third year? Interest rate is 12 %. Money is compounded every three-month.

 

12. A person needs 80,000 TL at the end of the fourth year. She wants to deposit her money into a six-month time deposit account. Interest rate for the first six-month is 8 %. Expected interest rate for the second six-month is 12 %. Expected interest rate for the third six-month is 14 %. Expected interest rate for the fourth six-month is 17 %. Expected interest rate for the third year is 15 %. Expected interest rate for the fourth year is 11 %. How much money does she have to deposit today so that she receives 80,000 TL at the end of the fourth year? Money is compounded every six-month.

 

13. Mr. A deposits his money into a time deposit account. Maturity is 3 months, interest rate is 10 %. What is the effective interest rate?

 

14. Monthly interest rate for an auto loan is 1.3 %. What is the annual simple interest rate? What is the effective interest rate?

 

15. Monthly interest rate for a real estate loan is 1.05 %. What is the annual simple interest rate? What is the effective interest rate?

 

16. Ä°ÅŸ Bank issues bill. Nominal value is 100 TL. Maturity is 206 days. Issue price is 95.46 TL.

 

      a.   What is the periodic interest rate (interest rate for 206 days)?

      b.   What is the annual simple interest rate?

      c.   What is the effective interest rate?

 

17. The price of a treasury note is 96 TL. There are 108 days until maturity. (Nominal value is 100 TL).

 

      a.   What is the periodic interest rate (interest rate for 108 days)?

      b.   What is the annual simple interest rate?

      c.   What is the effective interest rate?

 

18. The price of a discounted government bond is 90 TL. There are 410 days until maturity. (Nominal value is 100 TL).

 

      a.   What is the periodic interest rate (interest rate for 410 days)?

      b.   What is the annual simple interest rate?

      c.   What is the effective interest rate?

 

19. A person invests 30,000 TL into perpetuity. Interest rate is 10 %. What is the future value at the end of the fourth year?

 

20. A person invests 10,000 TL into perpetuity. Interest rate is 12 %. What is the future value in 50 days?

 

21. Annual simple interest rate is 10%. What is the effective interest rate of perpetuity?

 

22. The nominal interest rate of an investment is 14 %. Inflation is 8 %. What is the reel interest rate of this investment?

 

23. A person will invest 800 TL in every month into a fund. First payment will be made one month from now (ordinary annuity). If the interest rate is 10 %, how much money does he have at the end of the eighth year?

 

24. A person will invest 2,000 TL in every three-month into a fund. First payment will be made three months later (ordinary annuity). If the interest rate is 12 %, how much money does she have at the end of the tenth year?

 

25. A person will invest 500 TL in every month into a fund. First payment will be made now (annuity due). If the interest rate is 8 %, how much money does he have at the end of the ninth year?

 

26. A person will invest 2,500 TL in every three-month into a fund. First payment will be made now (annuity due). If the interest rate is 15 %, how much money does she have at the end of the 14^th year?

 

27. A person wants to receive 1,700 TL at the end of each month (ordinary annuity) for 8 years. If the interest rate is 12 %, how much money does he have to invest now?

 

28. A person wants receive 5,000 TL at the end of every three-month (ordinary annuity) for 17 years. If the interest rate is 14 %, how much money does he have to invest now?

 

29. A person takes out a real estate loan amounting 300,000 TL. Maturity is 10 years, monthly interest rate is 1.05 %. The loan will be paid in monthly payments. Payments will be made at the end of each month. What is the amount of the monthly payments?

 

30. A business takes out a long-term bank loan amounting 25,000,000 TL. Maturity is 8 years, interest rate is 14 %. The loan will be paid in six-month payments. Payments will be made at the end of each six-month. What is the amount of the six-month payments?

 

31. A company in tourism business takes out a loan amounting 350,000 TL to renovate its hotel for the summer season. Maturity is 24 months, interest rate is 14 %. The loan will be paid in monthly payments. Monthly payments will be made at the end of each month (ordinary annuity). The company wants to delay payments until summer when the cash flows are higher. So the company decided to delay the first three monthly payments. First payment will start at the end of the fourth month. What is the amount of the monthly payments?

 

32. A person is planning to invest a certain amount of money at the end of every three-month (ordinary annuity). That person wants to have 150,000 TL in this fund at the end of the tenth year. If the interest rate is 12 %, how much money does she have to invest at the end of every six-month?

 

33. A person is planning to invest a certain amount of money into a fund every month. The first payment will be made now (annuity due). That person wants to have 100,000 TL in this fund at the end of the fifth year. If the interest rate is 10 %, how much money does he have to invest every month beginning now?

 

34. Mrs. C is 30 years old now. Mrs. C wants to invest a certain amount of money at the beginning of every month into a pension fund for 30 years (until age 60). The first payment is made now. Mrs. C wants to receive 3,500 TL at the end of every month as an ordinary annuity for 20 years. How much money does she have to invest at the beginning of each month for 30 years? Interest rate when she makes the payments is 10 %, interest rate when she receives the payments is 8 %

 

35. You are working in the treasury department of a bank. Turkish Treasury announced that it would issue discounted bond. Nominal value is 100 TL, maturity is 395 days. If the required rate of return is 10 %, how much money do you offer for this bond? (What is the price of the bond?)

 

36. You are working in the treasury department of a bank. Turkish Treasury announced that it would issue a bond with coupon payments. Nominal value is 100 TL, maturity is 5 years. The bond makes coupon payments every six-month. Coupon rate is 8.5%. If the required rate of return is 9.2 %, how much money do you offer for this bond? (What is the price of the bond?)

 

37. Arçelik Corporation issues bond abroad. Nominal value is 100 Euro, maturity is 7 years. The bond makes coupon payments every year. Coupon rate is 3.875 %. What is the issue price if the required rate of return is 4 %.

 

38. A person buys government bond. Nominal value is 100 TL, maturity is 5 years.  The bond makes coupon payments every six-month. Coupon rate is 9 %, required rate of return is 7.5%. The bond has made six coupon payments until now. The person bought the bond on the coupon payment date. The person will receive the seventh coupon payment. What is the price of this bond?

 

39. A person buys government bond. Nominal value is 100 TL, maturity is 10 years.  The bond makes coupon payments every six-month. Coupon rate is 8.80 %, required rate of return is 10.5%. The bond has made 14 coupon payments until now. There are 105 days until the next coupon payment (six-month is 182 days). What is the price of this bond?

 

40. The government issued a government bond. Maturity is three years. Issue price is 95 TL (nominal value is 100 TL.). The bond makes coupon payments every three-month. Coupon rate is 10 %. How do you calculate yield to maturity of this bond?

 

41. The market price of a government bond is 100.80 TL now (nominal value is 100 TL). Maturity is 5 years. The bond makes coupon payments every six-month. Coupon rate is 12 %. The bond has made 4 coupon payments until now. There are 120 days until the next coupon payment (six-month is 182 days). How do you calculate yield to maturity of this bond?

 

42. The market price of a bond is 0.975 TL now (nominal value is 1 TL). Maturity is 3 years. The bond makes coupon payments every three-month. Coupon rate is 10 %. The bond has made 3 coupon payments until now. There are 25 days until the next coupon payment (three-month is 91 days). How do you calculate yield to maturity of this bond?