08 Jun Question Do not use the annuity tables in
Question
Do not use the annuity tables in the textbook to solve these problems. You are required to solve all problems in this course using a financial calculator. For each question you must show your work and provide the solution. For example:
You will need $80,000 annually for 20 years during retirement. How much will you need at retirement if you can earn a 4% rate of return?
PMT = 80,000
N = 20
I = 4
PV = 1,087,226
Rule of 72
• Tom invested $14,500 in an account he expects will earn 4% annually. Approximately how many years will it take for the account to double in value? 72 divided by 4 = 18 years
• Sam has $2,000 and he needs it to grow to $4,000 in 10 years. Assuming he adds no more money to this fund, what rate of return would he need to earn? 8%
Present Value
• Calculate the present value of $50,000 to be received in 13 years assuming an annual interest rate of 7%. PV= $20,748.22
• Calculate the present value of $30,000 to be received in 5 years assuming an annual interest rate of 10%, compounded monthly. $18,627.64
Future Value
• Calculate the future value of $10,000 invested for 30 years assuming an annual interest rate of 8%. the FV is 100, 626. 57
• Calculate the future value of $15,000 invested for 18 years assuming an annual interest rate of 11% compounded monthly.
PV Ordinary Annuity
• Calculate the present value of an ordinary annuity of $12,500 received quarterly for 25 years assuming a discount rate of 6%.
• Calculate the present value of an ordinary annuity of $5,000 received monthly for 20 years assuming a discount rate of 10%.
PV Annuity Due
• Calculate the present value of an annuity of $8,000 received quarterly that begins today and continues for 20 years, assuming a discount rate of 10%.
• Calculate the present value of an annuity of $5,000 received monthly that begins today and continues for 25 years, assuming a discount rate of 12%.
FV Ordinary Annuity
• Calculate the future value of an ordinary annuity of $4,000 paid every quarter for 10 years, assuming an annual earnings rate of 7%.
• Calculate the future value of an ordinary annuity of $750 paid every month for 30 years, assuming an annual earnings rate of 14%.
FV Annuity Due
• Calculate the future value of a quarterly annuity of $2,000 beginning todayand continuing for 15 years, assuming an annual earnings rate of 11%.
• Calculate the future value of a monthly annuity of $10 beginning today and continuing for 50 years, assuming an annual earnings rate of 12%.
Net Present Value (PV Uneven Payment Series ): See NPV Calculation Notes PowerPoint
• Calculate the NPV of a machine which is bought for $15,000, sold at the end of year 5 for $7,500.00, and produces the following cash flows: Year 1 $1,000, Year 2 $900, Year 3 $850, Year 4 $600, Year 5 $500, assume the cost of capital is 11%.
• Calculate the NPV of a machine which is bought for $6,000, sold at the end of year 5 for $2,000.00, and produces the following cash flows: Year 1 $2,000, Year 2 $1,750, Year 3 $1,500, Year 4 $1,000, Year 5 $500, assume the cost of capital is 8%.
Inflation Adjusted Return (PV of inflation-adjusted annuity due -BEG)
Don’t forget to use the inflation adjusted interest rate formula,
Inflation adjusted interest rate= [(1 + interest rate) / (1 + inflation rate) – 1] x 100
• Julie is ready to retire. She wants to receive the equivalent of $40,000 in today’s dollars at the beginning of each year for the next 25 years. She assumes inflation will average 3%, and she can earn a 10% after-tax return (compounded annually) on her investments. What lump sum does she need to invest today to attain her goal?
• Diane and Andy are ready to retire. They want to receive the equivalent of $75,000 in today’s dollars at the beginning of each year for the next 30 years. They assume inflation will average 3.5% over the long run, and they can earn a 9% after-tax return (compounded annually) on their investments. What lump sum do they need to invest today to attain their goal?
Internal Rate of Return (IRR)
• Jake borrowed $18,000 from his father to purchase a camper. Jake paid back $25,000 to his father at the end of 6 years. What was the average annual compound rate of interest on Jake’s loan from his father?
• Billy purchased a certificate of deposit 5 years ago for $1,000. If the certificate of deposit is due today in the amount of $2,000, what is the average annual compound rate of return assuming monthly compounding, that Billy realized on his investment?
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