1. Time Value of Money

2. Assume a couple puts $1,000 in the bank today. Their account earns 8% interest compounded annually. Assuming no other deposits were made, what will be the balance of the bank account at the end of 10 years?

3. Future Value of $1 PV (FV Factor) = FV $1,000 (n=10, i=8) $1,000 (2.159) = $2,159 At the end of 10 years, they would have $2,159 in the bank.

4. Assume a couple puts $1,000 in the bank today. Their account earns 8% interest compounded semi-annually. Assuming no other deposits were made, what will be the balance of the bank account at the end of 10 years?

5. Future Value of $1 PV (FV factor) = FV $1,000 (n=20, i=4) $1,000 (2.191) = $2,191 At the end of 10 years, they would have $2,191 in the bank.

6. Assume a couple wants to have $100,000 in the bank by the end of 15 years. They invest in an account that will pay 6% interest compounded annually. How much money do they need to deposit in the investment account today?

7. Present Value of $1 FV (PV Factor) = PV $100,000 (n=15, i=6%) $100,000 (.417) = $41,700 They should deposit $41,700 in the investment account today in order to have $100,000 at the end of 15 years.

8. Assume a couple wants to have $100,000 in the bank by the end of 15 years. They invest in an account that will pay 6% interest compounded semi-annually. How much money do they need to deposit in the investment account today?

9. Present Value of $1 FV (PV Factor) = PV $100,000 (n=30, i=3%) $100,000 (.412) = $41,200 They should deposit $41,200 in the investment account today in order to have $100,000 at the end of 15 years.

10. Assume a couple would like to set up an IRA account this taxable year. They choose to contribute $2,000 to the investment account at the end of each of the next 10 years. Their investment will earn 7% interest compounded annually. How much will they have at the end of 10 years?

11. Future Value of an Annuity Annuity (FVA Factor) = FV of Deposits and Interest $2,000 (n=10, i=7%) $2,000 (13.816) = $27,632 If they deposit $2,000 at the end of each of the next 10 years, and additionally earn 7% interest (compounded annually), they should have $27,632 at the end of the 10 year period.

12. You just won the lottery - $5,000,000. The State’s rules say that you may choose to receive the winnings in one of two ways. 1) You may choose to receive a check for $1,000,000 at the end of each of the next 5 years (annually). OR 2) You may choose to receive all the winnings in one check today equal to the present value of all 5 annual $1,000,000 payments. The current interest rate on investments is 6%

13. Present Value of an Annuity Annuity (PVA Factor) = PV of Deposits and Interest $1,000,000 (n=5, i=6) $1,000,000 (4.212) = $4,212,000 If you choose to receive all the winnings today equal to the present value of 5 annual payments – the check you receive today will be for $4,212,000.

14. Assume instead, the Lottery commission offered to pay you $500,000 every 6 months (semi-annually) for the next 5 years. At an annual interest rate of 6%, what would be the present value of that annuity assuming you chose to accept all the winnings in one check today.

15. Present Value of an Annuity Annuity (PVA Factor) = PV of Deposits and Interest $500,000 (n=10, i=3) $500,000 (8.530) = $4,265,000 If you choose to receive all the winnings today equal to the present value of 10 semi-annual payments of $500,000 – the check you receive today will be for $4,265,000.