Microsoft Word - Week 2__W

pdf

School

University of Wollongong *

*We aren’t endorsed by this school

Course

222

Subject

Finance

Date

Jan 9, 2024

Type

pdf

Pages

5

Uploaded by ProfessorLapwing6374

Report
FIN222 Week 2 Workshop Solution 1. What is the role of a financial system? A financial system consists of financial markets and financial institutions. A critical role of the financial system in the economy is to gather money from people and businesses with surplus funds to invest and channel money to those who need it. o Channel money from surplus units to deficit units 2. Consider an annuity consisting of three cash flows of $100 each. Assume a 10% interest rate. What is the present value of the annuity if the first cash flow occurs: 𝑃𝑉 ൌ 𝐶 𝑟 ሾ1 െ 1 ሺ1 ൅ 𝑟ሻ a) one year from today. 𝑃𝑉 ൌ 100 0.1 ൤1 െ 1 ሺ1.1ሻ ൨ ൌ 248.69 b) two years from today. 𝑃𝑉 ൌ 100 0.1 ൤1 െ 1 ሺ1.1ሻ 1.1 ൌ 226.08 c) three years from today. 𝑃𝑉 ൌ 100 0.1 ൤1 െ 1 ሺ1.1ሻ ሺ1.1ሻ ൌ 205.53 d) four years from today. 𝑃𝑉 ൌ 100 0.1 ൤1 െ 1 ሺ1.1ሻ ሺ1.1ሻ ൌ 186.84
3. You have decided to refinance your mortgage and plan to borrow whatever is outstanding on your current mortgage. The current monthly payment is $2000 and you have made every payment on time. The original term of the mortgage was 30 years, and the mortgage is exactly five years and eight months old. You have just made your monthly payment. The mortgage interest rate is 6% (APR). How much do you owe on the mortgage today? 𝑃𝑉 ൌ 𝐶 𝑟 ሾ1 െ 1 ሺ1 ൅ 𝑟ሻ Cൌ $2000, nൌ 30*12 – ሺ5*12൅8ሻ ൌ 292, rൌ 0.06/12ൌ 0.005 292 2000 1 PV ൌ 1 - ൌ $306,766.94 0.005 1.005 4. Suppose Capital One is advertising a 60-month, 6% APR motorcycle loan. If you need to borrow $8000 to purchase your dream Harley-Davidson, what will your monthly payment be? 𝑃𝑉 ൌ 𝐶 𝑟 ሾ1 െ 1 ሺ1 ൅ 𝑟ሻ Pൌ $8000, nൌ 60, rൌ 0.06/12ൌ 0.005 8000 ൌ 𝐶 0.005 ሾ1 െ 1 ሺ1.005ሻ ଺଴ 8000 ∗ 0.005 ሾ1 െ 1 ሺ1.005ሻ ଺଴ ൌ 𝐶 𝐶 ൌ $154.66
5. Assume that your superannuation fund promises you $40,000 per year starting when you retire 45 years from today (the first $40000 will come 45 years from now). If your discount rate is 7%, compounded annually, and you assume you will live for 15 years after retiring (so that you will get a total of 16 payments including the first one), what is the value today of the superannuation fund’s promise? 0 1 44 45 60 0 0 40,000 40,000 𝑃𝑉 ସସ 𝐶 𝑟 ሾ1 െ 1 ሺ1 ൅ 𝑟ሻ 𝑃𝑉 ସସ 40,000 0.07 ൤1 െ 1 ሺ1.07ሻ ଵ଺ ൨ ൌ $377,865.94 44 377, 865.94 PV ൌ ൌ $19, 250.92 ሺ1.07ሻ 6. You invest $150 in an investment fund today that pays 9 per cent interest per year. How long will it take to double your money? n n n n n FV ൌCሺ1൅rሻ 300ൌ150ሺ1.09ሻ 300 150ൌሺ1.09ሻ 2ൌሺ1.09ሻ lnሺ2ሻൌ lnሺ1.09ሻ lnሺ2ሻൌ nlnሺ1.09ሻ lnሺ2.00ሻ n ൌ ൌ 8.043 years lnሺ1.09ሻ
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help
7. You are now 50 years old and plan to retire at age 67. You currently have a share portfolio worth $150,000, a superannuation plan worth $250,000, and a money market account worth $50,000. Your share portfolio is expected to provide you annual returns of 12 per cent, your superannuation investment will earn you 9.5 per cent annually, and the money market account earns 6.25 per cent, compounded monthly. a. If you do not save another cent, what will be the total value of your investments when you retire at age 67? Share Portfolio FV ൌ 150000ሺ1.12ሻ ଵ଻ ൌ $1,029,906.13 Superannuation Investment FV ൌ 250000ሺ1.095ሻ ଵ଻ ൌ $1,169,445.63 Money market account FV ൌ 50000ሺ1 ൅ 0.0625/12ሻ ଵ଻௫ଵଶ ൌ $144,281.41 Total value of all three investments= $1,029,906.13+ $1,169,445.63+$144,281.41= $2,343,633.17 b. Assume that your superannuation contribution is $12,000 per year for the next 17 years (starting 1 year from now). Assume that your superannuation investment will earn you 9.5 per cent annually. How much will your investments be worth when you retire at 67? 𝐹𝑉 ൌ 𝐶 𝑟 ሾሺ1 ൅ 𝑟ሻ െ 1ሿ 𝐹𝑉 ൌ 12,000 0.095 ሾሺ1.095ሻ ଵ଻ െ 1ሿ ൌ $464,562 Total investment amount at retirement= $2,343,633.174+ $464,562.001 = $2,808,195.18 c. Assume that you expect to live another 23 years after you retire (until age 90). Using the balance from b with an interest rate of 8% per year, if you start withdrawing funds starting at age 68, how much can you withdraw every year with the final withdrawal made at age 90? 𝑃𝑉 ൌ 𝐶 𝑟 ሾ1 െ 1 ሺ1 ൅ 𝑟ሻ 2,808,195.18 ൌ 𝐶 0.08 ሾ1 െ 1 ሺ1.08ሻ ଶଷ 2,808,195.18 ∗ 0.08 ሾ1 െ 1 ሺ1.08ሻ ଶଷ ൌ 𝐶 $270,772.27 ൌ 𝐶
d. At age 67, you want your investments to support a perpetuity that starts a year from now. How much can you withdraw each year (at 8 per cent per year)? 𝑃𝑉 ൌ 𝐶 𝑟 2,808,195.18 ൌ 𝐶 0.08 2,808,195.18 ∗ 0.08 ൌ 𝐶 $224,655.61 ൌ 𝐶