1. Quantitative Finance Unit 1 Financial Mathematics

2. Unit IFinancial Mathematics Introduction, Time Value of Money, Time line, Cash Flow Sign Convention, Annuities

3. Financial Mathematics 1.PV of lump sum amount 2.PV of annuity 3.PV of annuity due 4.FV of lump sum amount 5.FV of annuity 6.FV of annuity due 7.Sinking Fund 8.Loan amortization 9.Effective vs nominal rate of interest 10.Perpetuity 11.Doubling period

4. Financial Mathematics using excel 1.PV of lump sum amount – using pv function 2.PV of annuity- using pv function 3.PV of annuity due – using pv function 4.FV of lump sum amount – using fv function 5.FV of annuity - using fv function 6.FV of annuity due - using fv function 7.Sinking Fund – using pmt function 8.Loan amortization – using pmt function 9.Effective vs nominal rate of interest – using rate function 10.Perpetuity - 11.Doubling period – using nper function

5. You are planning to retire in twenty years. You'll live ten years after retirement. You want to be able to draw out of your savings at the rate of Rs.10,000 per year. How much would you have to pay in equal annual deposits until retirement to meet your objectives? Assume interest remains at 9%.

6. You can deposit Rs.4000 per year into an account that pays 12% interest. If you deposit such amounts for 15 years and start drawing money out of the account in equal annual installments, how much could you draw out each year for 20 years?

7. 1.Construct an amortization schedule for a 3- year loan of Rs.20,000 if interest is 9%. 2.Your company must deposit equal annual beginning of year payments into a sinking fund for an obligation of Rs.800,000 which matures in 15 years. Assuming you can earn 4% interest on the sinking fund, how much must the payments be?

8. Exercise 1 1.What is the value of a Rs.100 perpetuity if interest is 7%? 2.You deposit Rs.13,000 at the beginning of every year for 10 years. If interest is being paid at 8%, how much will you have in 10 years? 3.You are getting payments of Rs.8000 at the beginning of every year and they are to last another five years. At 6%, what is the value of this annuity? 4.How much would you have to deposit today to have Rs.10,000 in five years at 6% interest compounded semiannually?

9. 5.If you get payments of Rs.15,000 per year for the next ten years and interest is 4%, how much would that stream of income be worth in present value terms? 6.If you deposit Rs.45,000 into an account earning 4% interest compounded quarterly, how much would you have in 5 years? 7.How much would you pay for an investment which will be worth Rs.16,000 in three years? Assume interest is 5%. 8.You have Rs.100,000 to invest at 4% interest. If you wish to withdraw equal annual payments for 4 years, how much could you withdraw each year and leave Rs.0 in the investment account?

10. Exercise 2 1.Rs.7,000 dollars 10 years from now at 7% is worth how much today? 2.Rs.10,000 dollars 7 years from now at 10% is worth how much today? 3.How much would you have to put in the bank today at 5% to accumulate Rs.1,000 by next year? 4.If you double your money in 5 years, what interest rate did you earn?

11. 4.If you triple your money in 10 years, what interest rate did you earn? 5.If you put Rs.100 in the market at the end of every year for 20 years at 10%, how much would you end up with? What if you put the Rs.100 in at the beginning of every year? 6.If you put Rs.100 in the market today at 10%, how much would you end up with in 20 years?

12. 7.If you borrow Rs.10,000 for a car loan at a 6% simple annual interest rate, what would be your monthly payment on a 5 year loan? 8.If you borrow Rs.150,000 for a house at a 8% simple annual interest rate for 30 years, what is your monthly payment? 9.If you want a Rs.1,000,000 for retirement in 30 years, how much would you have to save by the end of each year if you could make 12% per year? How much would you have to set aside each year if you could put money away starting now? 10.If you put Rs.5000 in the stock market, how many years would it take you to triple your money if the market is making 12% a year?

13. 11.If the effective annual interest rate is 8.5% per year, what is the nominal annual interest rate under monthly compounding? 12.If you put Rs.10 away at the end of each month for the next 40 years at a 12% simple annual interest rate, how much money would you end up with? What if you started at the beginning of each month? 13.If you borrow Rs.150,000 for a house at 8% simple annual interest rate for 15 years, what is your monthly payment? 14.Referring to question 17, how much interest did you pay over the 15 years?

14. Exercise 3 1.The present value of a single future sum a.increases as the number of discount periods increases. b.is generally larger than the future sum. c.depends upon the number of discount periods. d.increases as the discount rate increases

15. 2.At 8 percent compounded annually, how long will it take Rs.750 to double? a.6.5 years b.48 months c.9 years d.12 years

16. 3.If the interest rate is zero: a.PV = FV n b.PV = FV n c.FV = PV d.FV = PV/e n

17. You wish to borrow Rs.2,000 to be repaid in 12 monthly installments of Rs.189.12. The annual interest rate is: a.24 percent. b.8 percent. c.18 percent. d.12 percent.

18. If you have Rs.20,000 in an account earning 8 percent annually, what constant amount could you withdraw each year and have nothing remaining at the end of 5 years? a.Rs.3,525.62 b.Rs.5,009.13 c.Rs.3,408.88 d.Rs.2,465.78

19. You just purchased a parcel of land for Rs.10,000. If you expect a 12 percent annual rate of return on your investment, how much will you sell the land for in 10 years? a.Rs.25,000 b.Rs.31,060 c.Rs.38,720 d.Rs.34,310

20. A commercial bank will loan you Rs.7,500 for two years to buy a car. The loan must be repaid in 24 equal monthly payments. The annual interest rate on the loan is 12 percent of the unpaid balance. How large are the monthly payments? a.Rs.282.43 b.Rs.390.52 c.Rs.369.82 d.Rs.353.05

21. 8.Which of the following provides the greatest annual interest? a.10% compounded annually b.9.5% compounded monthly c.9% compounded daily

22. 9.If you place Rs.50 in a savings account with an interest rate of 7% compounded weekly, what will the investment be worth at the end of five years (round to nearest dollar)? a.Rs.72 b.Rs.70 c.Rs.71 d.Rs.57

23. 10.What is the annual compounded interest rate of an investment with a stated interest rate of 6% compounded quarterly for 7 years (round to the nearest.1%)? a.51.7% b.6.7% c.10.9% d.6.1%

24. 11.If you put Rs.600 in a savings account that yields an 8% rate of interest compounded weekly, what will the investment be worth in 37 weeks (round to the nearest dollar)? a.Rs.648 b.Rs.635 c.Rs.634 d.Rs.645

25. 12.What is the value of Rs.750 invested at 7.5% compounded quarterly for 4.5 years (round to nearest Rs.1)? a.Rs.1,048 b.Rs.1,010 c.Rs.1,038 d.Rs.808

26. 13.If you put Rs.900 in a savings account that yields 10% compounded semi-annually, how much money will you have in the account in three years (round to nearest dollar)? a.Rs.1,340 b.Rs.1,170 c.Rs.1,227 d.Rs.1,206

27. 14.Which of the following provides the greatest annual yield? a.16% compounded quarterly b.15.2% compounded monthly c.15.2% compounded daily d.cannot be determined

28. 15.How much would Rs.1,000 in an account paying 14 percent interest compounded semi- annually accumulate to in 10 years? a.Rs.2,140 b.Rs.3,707 c.Rs.1,647 d.Rs.3,870

29. 16.If you want to have Rs.90 in four years, how much money must you put in a savings account today? Assume that the savings account pays 8.5% and it is compounded monthly (round to the nearest Rs.1). a.Rs.64 b.Rs.65 c.Rs.66 d.Rs.71

30. 17.What is the present value of Rs.12,500 to be received 10 years from today? Assume a discount rate of 8% compounded annually and round to the nearest Rs.10. a.Rs.5,790 b.Rs.11,574 c.Rs.9,210 d.Rs.17,010

31. 18.If you want to have Rs.1,200 in 27 months, how much money must you put in a savings account today? Assume that the savings account pays 14% and it is compounded monthly (round to nearest Rs.10). a.Rs.910 b.Rs.890 c.Rs.880 d.Rs.860

32. 19.If you want to have Rs.2,100 in 3 years, how much money must you put in a savings account today? Assume that the savings account pays 7% and it is compounded quarterly. a.Rs.1,656 b.Rs.1,705 c.Rs.1,674 d.Rs.1,697

33. 20.What is the present value of an annuity of Rs.27 received at the beginning of each year for the next six years? The first payment will be received today, and the discount rate is 10% (round to nearest Rs.10). a.Rs.120 b.Rs.130 c.Rs.100 d.Rs.110

34. 21.What is the present value of Rs.250 received at the beginning of each year for 21 years. Assume that the first payment is received today. Use a discount rate of 12%, and round your answer to the nearest Rs.10. a.Rs.1,870 b.Rs.2,090 c.Rs.2,120 d.Rs.2,200

35. 22.What is the present value of an annuity of Rs.100 received at the end of each year for seven years? The first payment will be received one year from today (round to nearest Rs.10). The discount rate is 13%. a.Rs.440 b.Rs.43 c.Rs.500 d.Rs.1,040

36. 23.What is the present value of annuity of an Rs.50 received at the end of each year for 3 years? Assume a discount rate of 11%. The first payment will be received one year from today (round to nearest Rs.1). a.Rs.68 b.Rs.122 c.Rs.136 d.Rs.110

37. 24.You are considering two investments: A & B. Both investments provide a cash flow of Rs.100 per year for n years. However, investment A receives the cash flow at the beginning of each year, while investment B receives the cash at the end of each year. If the present value of cash flows from investment A is P, and the discount rate is r, what is the present value of the cash flows from investment B? a.P/(1+r) b.P(1+r) c.P/(1+r) n d.P(1+r) n

38. 25.What is the value on 1/1/85 of the following cash flows: Date Cash Received Amount of Cash 1/1/87 Rs.100 1/1/88 Rs.200 1/1/89 Rs.100 1/1/90 Rs.100 1/1/91 Rs.100 Use a 10% discount rate, and round your answer to the nearest Rs.10. a.Rs.490 b.Rs.460 c.Rs.420 d.Rs.450

39. 26.Charlie Stone wants to retire in 30 years, and he wants to have an annuity of Rs.1000 a year for 20 years after retirement. Charlie wants to receive the first annuity payment at the end of the 30th year. Using an interest rate of 10%, how much must Charlie invest today in order to have his retirement annuity (round to nearest Rs.10). a.Rs.500 b.Rs.490 c.Rs.540 d.Rs.570

40. 27.If you put Rs.510 in a savings account at the beginning of each year for 30 years, how much money will be in the account at the end of the 30th year? Assume that the account earns 5% and round to the nearest Rs.100. a.Rs.33,300 b.Rs.32,300 c.Rs.33,900 d.none of the above

41. 28.If you put Rs.310 in a savings account at the beginning of each year for 10 years, how much money will be in the account at the end of the 10th year? Assume that the account earns 5.5% and round to the nearest Rs.100. a.Rs.3,800 b.Rs.3,900 c.Rs.4,000 d.Rs.4,200

42. 29.How much money must you pay into an account at the beginning of each of 30 years in order to have Rs.10,000 at the end of the 30th year? Assume that the account pays 11% per annum, and round to the nearest Rs.1. a.Rs.39 b.Rs.46 c.Rs.50 d.none of the above

43. 30.How much money must you pay into an account at the beginning of each of 5 years in order to have Rs.5,000 at the end of the 5th year? Assume that the account pays 12% per year, and round to the nearest Rs.10. a.Rs.700 b.Rs.1,390 c.Rs.1,550 d.Rs.790

44. 31.You are going to pay Rs.800 into an account at the beginning of each of 20 years. The account will then be left to compound for an additional 20 years. At the end of the 41st year you will begin receiving a perpetuity from the account. If the account pays 14%, how much each year will you receive from the perpetuity (round to nearest Rs.1,000)? a.Rs.140,000 b.Rs.150,000 c.Rs.160,000 d.Rs.170,000

45. 32.You are going to pay Rs.100 into an account at the beginning of each of the next 40 years. At the beginning of the 41st year you buy a 30 year annuity whose first payment comes at the end of the 41st year (the account pays 12%). How much will you receive at the end of the 41st year (i.e. the first annuity payment). Round to nearest Rs.100. a.Rs.93,000 b.Rs.7,800 c.Rs.11,400 d. Rs.10,700