time value of money. assume a couple puts $1,000 in the bank today. their account earns 8% interest...

Time Value of MoneyTime Value of Money

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?

Future Value of $1Future 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.

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?

Future Value of $1Future 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.

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?

Present Value of $1Present 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.

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?

Present Value of $1Present 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.

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?

Future Value of an AnnuityFuture 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.

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).

OR2) 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%

Present Value of an Present Value of an AnnuityAnnuity

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.

• 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.

Present Value of an AnnuityPresent 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.