Time Value of Money Extra Problem Set 11. 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 $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%. [$1254] 

2. You can deposit $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? [$19964.12] 

3. What is the value of a $100 perpetuity if interest is 7%? [$1428.57] 

4. You deposit $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? [$203391.33] 

5. You are getting payments of $8000 at the beginning of every year and they are to last another five years. At 6%, what is the value of this annuity? [35720.84] 

6. How much would you have to deposit today to have $10,000 in five years at 6% interest compounded semiannually? [$7440.94] 

7. Construct an amortization schedule for a 3-year loan of $20,000 if interest is 9%.  

8. If you get payments of $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? [$121663.50] 

9. Your company must deposit equal annual beginning of year payments into a sinking fund for an obligation of $800,000 which matures in 15 years. Assuming you can earn 4% interest on the sinking fund, how much must the payments be? [$38415] 

10. If you deposit $45,000 into an account earning 4% interest compounded quarterly, how much would you have in 5 years? [$54908.55] 

11. How much would you pay for an investment which will be worth $16,000 in three years? Assume interest is 5%. [$13821] 

12. You have $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 $0 in the investment account? [$27548] 

13. You are considering the purchase of two different insurance annuities. Annuity A will pay you $16,000 at the beginning of each year for 8 years. Annuity B will pay you $12,000 at the end of each year for 12 years. Assuming your money is worth 7%, and each costs you $75,000 today, which would you prefer? [$102228 and $95312] 

14. If your company borrows $300,000 at 8% interest and agrees to repay the loan in 10 equal semiannual payments to include principal plus interest, how much would those payments be? [$36897] 

15. You deposit $17,000 each year for 10 years at 7%. Then you earn 9% after that. If you leave the money invested for another 5 years how much will you have in the 15th year? [$361374]

Time Value of Money Extra Problem Set 2

1. $7,000 dollars 10 years from now at 7% is worth how much today? 2. $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 $1,000 by next year? 4. If you double your money in 5 years, what interest rate did you earn? 5. If you triple your money in 10 years, what interest rate did you earn? 6. If you put $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 $100 in at the beginning of every year? 7. If you put $100 in the market today at 10%, how much would you end up with in 20 years? 8. If you borrow $10,000 for a car loan at a 6% simple annual interest rate, what would be your monthly payment on a 5 year loan? 9. If you borrow $150,000 for a house at a 8% simple annual interest rate for 30 years, what is your monthly payment? 10. A simple annual interest rate of 12% compounded monthly has an effective yield of? 11. A simple annual interest rate of 12% compounded quarterly has an effective yield of? 12. A simple annual interest rate of 12% compounded semi-annually is an effective yield of? 13. If you want a $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? 14. If you put $5000 in the stock market, how many years would it take you to triple your money if the market is making 12% a year? 15. If the effective annual interest rate is 8.5% per year, what is the nominal annual interest rate under monthly compounding? 16. If you put $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? 17. If you borrow $150,000 for a house at 8% simple annual interest rate for 15 years, what is your monthly payment? 18. Referring to question 17, how much interest did you pay over the 15 years? 19. What is the value of a $10,000,000 lottery ticket paid out over 20 years if interest rates are at 6%, the average tax rate is 35%, and the odds of winning are 1/7,000,000? 20. How long would it take to accumulate $50,000 if you started putting $5 in the bank every day starting at the end of today at simple annual interest rate of 7.3%? 21. How long would it take to accumulate $50,000 if you started putting $5 in the bank every month starting now at a simple annual interest rate of 7.3%? What if you started at the end of each month?

Answers:1. 3,5582. 5,1313. 9524. 14.875. 11.66. 5,727, 6,3007. 6738. 1939. 1,10010. 12.6811. 12.5512. 12.3613. 4,144, 3,69914. 9.715. 8.1916. 117,647, 118,82417. 1,43318. 108,02619. Value of winning is 6,079,058. After tax is 0.65 * 6,079,058 = 3,951,387. Expected value is then 1/7,000,000 * 3,951,387 = $.56. Thus, the expected value of the $1 ticket is only 56 cents. That’s how the state makes money! Plus most states only pay out 50% of all receipts so they are already up 10,000,000 to start with.20. 5,493 days21. 679 months, 680 months

Time Value of Money Extra Multiple Choice Practice Questions

 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

 2. At 8 percent compounded annually, how long will it take $750 to double?

a. 6.5 yearsb. 48 monthsc. 9 yearsd. 12 years

 3. If the interest rate is zero:

a. PV = FVn

b. PV = FVn

c. FV = PVd. FV = PV/en

 

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

 5. If you have $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. $3,525.62b. $5,008.76c. $3,408.88d. $2,465.78

 6. You just purchased a parcel of land for $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. $25,000b. $31,060c. $38,720d. $34,310

 7. A commercial bank will loan you $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. $282.43b. $390.52c. $369.82d. $353.05

 8. Which of the following provides the greatest annual interest?

a. 10% compounded annuallyb. 9.5% compounded monthlyc. 9% compounded daily

 9. If you place $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. $72b. $70c. $71d. $57

 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%

 11. If you put $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. $648b. $635c. $634d. $645

 

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

 13. If you put $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. $1,340b. $1,170c. $1,227d. $1,206

 14. Which of the following provides the greatest annual yield?

a. 16% compounded quarterlyb. 15.2% compounded monthlyc. 15.2% compounded dailyd. cannot be determined

 15. How much would $1,000 in an account paying 14 percent interest compounded semi-

annually accumulate to in 10 years?a. $2,140b. $3,707c. $1,647d. $3,870

 16. If you want to have $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 $1).a. $64b. $65c. $66d. $71

 17. What is the present value of $12,500 to be received 10 years from today? Assume a

discount rate of 8% compounded annually and round to the nearest $10.a. $5,790b. $11,574c. $9,210d. $17,010

 18. If you want to have $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 $10).a. $910b. $890c. $880d. $860

 

19. If you want to have $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. $1,656b. $1,705c. $1,674d. $1,697

 20. What is the present value of an annuity of $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 $10).a. $120b. $130c. $100d. $110

 21. What is the present value of $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 $10.a. $1,870b. $2,090c. $2,120d. $2,200

 22. What is the present value of an annuity of $100 received at the end of each year for seven

years? The first payment will be received one year from today (round to nearest $10). The discount rate is 13%.a. $440b. $43c. $500d. $1,040

 23. What is the present value of annuity of an $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 $1).a. $68b. $122c. $136d. $110

 

24. You are considering two investments: A & B. Both investments provide a cash flow of $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

 25. What is the value on 1/1/85 of the following cash flows:

Date Cash Received Amount of Cash 1/1/87 $100 1/1/88 $200 1/1/89 $100 1/1/90 $100 1/1/91 $100 Use a 10% discount rate, and round your answer to the nearest $10.a. $490b. $460c. $420d. $450

 26. Charlie Stone wants to retire in 30 years, and he wants to have an annuity of $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 $10).a. $500b. $490c. $540d. $570

 27. If you put $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 $100.a. $33,300b. $32,300c. $33,900d. none of the above

 28. If you put $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 $100.a. $3,800b. $3,900c. $4,000d. $4,200

 29. How much money must you pay into an account at the beginning of each of 30 years in

order to have $10,000 at the end of the 30th year? Assume that the account pays 11% per annum, and round to the nearest $1.a. $39b. $46c. $50d. none of the above

 30. How much money must you pay into an account at the beginning of each of 5 years in

order to have $5,000 at the end of the 5th year? Assume that the account pays 12% per year, and round to the nearest $10.a. $700b. $1,390c. $1,550d. $790

 31. You are going to pay $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 $1,000)?a. $140,000b. $150,000c. $160,000d. $170,000

 32. You are going to pay $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 $100.a. $93,000b. $7,800

c. $11,400d. $10,700

 Answers 1. c2. c3. c4. a5. b6. b7. d8. a9. c10. d11. b12. a13. d14. a15. d16. a17. a18. c19. b20. b21. c22. a23. b24. a25. c26. c27. d28. d29. b30. a31. c32. d