Time 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?
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.
Future Value of $1

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?
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.
Future Value of $1

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?
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.
Present Value of $1

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?
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.
Present Value of $1

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?
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.
Future Value of an Annuity

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%
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.
Present Value of an Annuity
•
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.
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.
Present Value of an Annuity