HW 1 Finance

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Hofstra University *

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Course

101

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Finance

Date

Jan 9, 2024

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pdf

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1

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1 Name: __________________ FIN 101-A Introduction to Finance, Financial Markets and Institutions Homework Assignment 1 (Practice Problem Set) Part I. 1. Suppose Bill invests $1,000 for 6 years at 8% interest rate. How much would Bill have? NPER Rate PV FV 6 8% 1000 $1,586.87 2. About 390 years ago, the Dutch bought all of Manhattan island for about $24 worth of trinkets and beads. Assuming the annual interest rate is 8.5%, how much does these $24 worth today? NPER Rate PV FV 390 8.50% 24 $1,576,918,084,076,100 3. What is the future value of $6,200 invested for 23 years at 6.25 percent compounded annually? NPER Rate PV FV 23 6.25% 6200 $25,001 4. Suppose Nancy needs $15,000 in two years for the down payment on a new car. If Nancy can earn 7% annually, how much does she need to invest today? NPER Rate PV FV 2 7% $13,101.58 15000 5. Tom wants to begin saving for his daughter’s college education and he estimates that she will need $20,000 in 17 years. If Tom feels confident that he can earn 5.5% per year, how much does Tom need to invest today? NPER Rate PV FV 17 5.50% $8,048.93 20000 6. Your parents set up a trust fund for you 10 years ago that is now worth $250,000. If the fund earned 7.3% per year, how much did your parents invest? NPER Rate PV FV 10 7.30% $123,578.46 250000 2 7. Your father invested a lump sum 26 years ago at 5.25 percent annual interest. Today, he gave you the proceeds of that investment which totaled $51,480.79. How much did your father originally invest? NPER Rate PV FV 26 5.25% $13,610.39 51,480.79 8. Forty years ago, your mother invested $6,000. Today, that investment is worth $430,065.11. What is the average annual rate of return she earned on this investment? NPER Rate PV FV 40 11.27% 6000 430,065.11 9. Ben is looking at an investment that will pay $1,500 in 4 years if he invests $1,000 today. What is the implied rate of interest? (Please keep two decimal places.) NPER Rate PV FV 4 10.67% 1000 1500 10. Suppose Daniel is offered an investment that will allow him to triple his money in 8 years. He has $10,000 to invest. What is the implied rate of interest? (Please keep two decimal places.) NPER Rate PV FV 8 14.72% 10000 30000 11. You want to purchase a new car, and you are willing to pay $25,000. If you can invest at 12% per year and you currently have $18,000, how long will it be before you have enough money to pay cash for the car? (Please keep two decimal places.) NPER Rate PV FV 2.90 12% 18000 25000 12. On your ninth birthday, you received $300 which you invested at 5.5 percent interest, compounded annually. Your investment is now worth $756. How old are you today? (Please keep the integer only.) NPER Rate PV FV 17 5.50% 300 756 Age = 9 + 17 = 26 (27 is also acceptable.) 3 Part II. While I demonstrate below how to use Excel to solve TVM-related questions, please also practice using a financial calculator to solve these problems. 13. (FV with multiple cash flows) You expect to receive two cash flows: $33,000 paid in 5 years and $49,500 paid in 10 years. You'll put the money into a savings account with an annual interest rate of 2%. What is the future value of the combined cash flows in 15 years? Solutions: 4 14. (FV with multiple cash flows) Wells Fargo offers a new savings product: You make the following payments at the end of each year and will then receive a lump sum payment 35 years from now. Year Payment 1 300 2 400 3 500 4 600 5 700 The annual interest rate is 7%. What is the future value of your investment in year 35? Solutions: 6 16. (PV with multiple cash flows) It is the end of 2022. You played the lottery and won the following cash flows, to be paid at the end of each year: Assuming the interest rate is 10%. What is the present value of all cash flows? Solutions: 7 17. (Perpetuity) The preferred stock of General Motors pays an annual dividend of $1.1 forever. The appropriate discount rate is 6% per year. What is the present value of all dividends? Solutions: Since this is a perpetuity (constant payment forever), the present value is: PV = PMT/r = 1.1 / 0.06 = 18.33 18. (Annuity PV) If you expect to receive the $2 every quarter for exactly 2 years and nothing thereafter, what is the present value of those cash flows? (Assume the quarterly interest rate is 4%.) Solutions: Since this is a contant cash flow for a specified number of periods, it's an annuity and we can use the annuity Excel formula. Using Excel (do not enter the thousands separators): =PV(rate, nper, pmt, fv) =PV(0.04, 8, -2) =13.465 19. (Annuity PV) You want to buy a house financed with a 30-year fixed-rate mortgage. The best monthly interest rate you could find is 1.1%. What is the most you can borrow if you can only afford to pay $1,400 per month? Solutions: Using Excel (do not enter the thousands separators): =PV(rate, nper, pmt) =PV(0.011, 360, -1,400) =124,793 20. (Annuity PV) You took out a student loan in college and now have to pay $700 every year for 20 years, starting one year from now. The annual interest rate on the loan is 4%. What is the present value of the 20 yearly payments? Solutions: Using Excel (do not enter the thousands separators): =PV(rate, nper, pmt) =PV(0.04, 20, -700) =9,513 This is the outstanding balance on your loan, i.e., your debt.
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