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 today and 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?