Chapter 5 Time Value of Moey 1. Suppose you deposit $100 i a bak that pays 10% iterest per year. How much will you have i the bak oe year later? 2. Suppose you deposit $100 i a bak that pays 10% per year. How much will you have i the bak two years later? Future value of a sigle cash flow: FV PV ( 1 i) 3. Suppose you deposit $100 i a bak that pays 15% per year. How much will you have i the bak two years later? Note: All else beig the same, as the iterest rate icreases, the future value, ad as the umber of periods icreases, the future value. 4. Suppose you deposit $100 oe year from ow, ad $200 two years from ow. How much will you have i the bak 4 years from today if the iterest rate is 8% per year? 5. If a deposit of $250 today grows to $341.91 i three years, what is the aual iterest rate eared?
6. If the iterest rate is 6% per year, how log will it take to triple your moey? 7. Fid the preset value of $200 to be received oe year from today if the iterest rate is 10% per year. Preset value of a sigle cash flow: PV FV FV (1 i (1 i) ) 8. Fid the preset value of $200 to be received two years from today if the iterest rate is 10% per year. 9. Fid the preset value of $200 to be received two years from today if the iterest rate is 15% per year. Note: All else beig the same, as the iterest rate icreases, the preset value, ad as the umber of periods icreases, the preset value. 10. Fid the preset value of the followig cash flows, assumig a iterest rate of 10% per year. CF2 = +$200; CF3 = -$100; CF4 = +$600
A Auity is a series of paymets of a equal amout at fixed itervals for a specified umber of periods. A ordiary auity has paymets at the ed of each period. 11. If you deposit $100 per year at the ed of each of the ext 3 years, how much will you have i the accout three years from today (i.e. just after you make the last deposit) if the bak pays 10% per year? Future value of a ordiary auity: FVA (1 i) PMT i 1 12. You wish to accumulate $6,000 four years from today. How much should you deposit at the ed of each year if the bak pays 10% per year? 13. How much should you deposit today i order to be able to withdraw $100 at the ed of each of the ext three years, if the iterest rate is 10% per year? 1 1 (1 i) Preset Value of a Ordiary Auity: PVA PMT i 1 (1 i) PMT i
14. Costruct a loa amortizatio table for a $5,000 loa at 10% to be repaid i four equal ed-of-year istallmets. Year Begiig Balace Iterest Paymet Pricipal Repaid 1 2 3 4 Edig Balace For the loa i the above problem, what is the remaiig balace after three paymets have bee made? A perpetuity is a stream of equal paymets expected to cotiue forever. 14. Fid the preset value of a perpetuity of $1,200 per year if the iterest rate is 10% per year. Preset value of a perpetuity: PMT PVP i
15. Suppose the stated iterest rate is 12% per year. Fid the future value of $1,000 oe year later if iterest is compouded: a. aually b. semi-aually c. mothly d. daily What is the effective aual rate i each case? i % 1 NOM EFF 1.0 M M 16. Suppose you deposit $100 every moth i a accout that has a stated rate of 9% per year compouded mothly. How much will you have after three years? 17. Suppose you deposit $1,200 every year i a accout that has a stated rate of 9% per year compouded mothly. How much will you have after three years?
A auity due has paymets at the begiig of each period. 18. Suppose you deposit $200 at the begiig of each of the ext three years. How much will you have three years from today if the iterest rate is 10% per year? Future value of a auity due: (1 i) 1 FVADue FVAordiary( 1 i) PMT (1 i) i 19. Fid the preset value of a three year auity with begiig-of-year cash flows of $200 each, assumig a iterest rate of 10% per year. Preset value of a auity due: 1 (1 i) PVADue PVAordiary( 1 i) PMT (1 i) i 20. You have deposited $100,000 today i a accout that pays 10% iterest per year. You pla o makig a roud-the-world trip 4 years from today, which will cost $30,000 at that time. You also pla o makig equal aual withdrawals i each of the ext ie years, begiig oe year from today. Fid the amout of the aual withdrawal.
21. You wish to have $2.0 millio o the day you retire 20 years from today. You pla o savig a equal aual amout every year to reach your goal. All savigs will be ivested i a stock mutual fud, which you expect will ear about 12% per year. How much should you save aually? 22. To fiace the purchase of your house, you borrow $150,000 for 30 years at a stated rate of 9% per year. a. What is the amout of your mothly paymet? b. What is the total iterest paid o this loa? 23. Your bak offers you a CD for $2,000, redeemable i 22 moths for $2,232. What is the APR (Aual Percetage Rate, or omial iterest rate)? What is the EFF% (Effective aual rate)?