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**Unformatted text preview: **ter’s college education and you
estimate that she will need $150,000 in 17
years. If you feel confident that you can
earn 8% per year, how much do you need
to invest today?
to PV = 150,000 / (1.08)17 = 40,540.34 14
14 Present Values – Example 3 Your parents set up a trust fund for you 10
Your years ago that is now worth $19,671.51. If
the fund earned 7% per year, how much
did your parents invest?
did PV = 19,671.51 / (1.07)10 = 10,000 15
15 Present Value – Important
Present
Relationship I
Relationship For a given interest rate – the longer the
For time period, the lower the present value
time What is the present value of $500 to be
What
received in 5 years? 10 years? The discount
rate is 10%
rate
5 years: PV = 500 / (1.1)5 = 310.46
10 years: PV = 500 / (1.1)10 = 192.77 16
16 Present Value – Important
Present
Relationship II
Relationship For a given time period – the higher the
For interest rate, the smaller the present
value
value What is the present value of $500 received
What
in 5 years if the interest rate is 10%? 15%?
in
• Rate = 10%: PV = 500 / (1.1)5 = 310.46
• Rate = 15%; PV = 500 / (1.15)5 = 248.59 17
17 Quick Quiz – Part II What is the relationship between present value
What
and future value?
and
Suppose you need $15,000 in 3 years. If you
Suppose
can earn 6% annually, how much do you need to
invest today?
invest
If you could invest the money at 8%, would you
If
have to invest more or less than at 6%? How
much?
much? 18
18 The Basic PV Equation The
Refresher
Refresher PV = FV / (1 + r)t
There are four parts to this equation PV, FV, r and t
If we know any three, we can solve for the fourth If you are using a financial calculator, be sure
If
and remember the sign convention or you will
receive an error (or a nonsense answer) when
solving for r or t
solving 19
19 Discount Rate Often we will want to know what the implied
Often
interest rate is in an investment
interest
Rearrange the basic PV equation and solve for r FV = PV(1 + r)t
r = (FV / PV)1/t – 1 If you are using formulas, you will want to make
If
use of both the yx and the 1/x keys
use 20
20 Discount Rate – Example 1 You are looking at an investment that will pay
You
$1,200 in 5 years if you invest $1,000 today.
What is the implied rate of interest?
What r = (1,200 / 1,000)1/5 – 1 = .03714 = 3.714%
Calculator –...

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