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**Unformatted text preview: **year 5?
What is the value of the cash flows today?
What is the value of the cash flows at year 3? 15
15 Annuities and Perpetuities
Annuities
Defined
Defined Annuity – finite series of equal payments that
Annuity
occur at regular intervals
occur If the first payment occurs at the end of the period, it
If
is called an ordinary annuity
is
If the first payment occurs at the beginning of the
If
period, it is called an annuity due
period, Perpetuity – infinite series of equal payments 16
16 Annuities and Perpetuities –
Annuities
Basic Formulas
Basic Perpetuity: PV = C / r Annuities:
1 1− (1 + ) t r
PV = C r 1 + )t − (
r
1
FV = C r 17
17 Annuity – Example 6.5 You borrow money TODAY so you need to
You
compute the present value.
compute 48 N; 1 I/Y; -632 PMT; CPT PV = 23,999.54
48
($24,000)
($24,000) Formula:
1 1− (1.01) 48
PV = 632 .01 = 23,999.54 18
18 Annuity – Sweepstakes
Annuity
Example
Example Suppose you win the Publishers Clearinghouse
Suppose
$10 million sweepstakes. The money is paid in
equal annual installments of $333,333.33 over
30 years. If the appropriate discount rate is 5%,
how much is the sweepstakes actually worth
today?
today? PV = 333,333.33[1 – 1/1.0530] / .05 = 5,124,150.29 19
19 Buying a House You are ready to buy a house and you have $20,000
You
for a down payment and closing costs. Closing costs
are estimated to be 4% of the loan value. You have an
annual salary of $36,000 and the bank is willing to
allow your monthly mortgage payment to be equal to
28% of your monthly income. The interest rate on the
loan is 6% per year with monthly compounding (.5%
per month) for a 30-year fixed rate loan. How much
money will the bank loan you? How much can you offer
for the house?
for 20
20 Buying a House - Continued Bank loan Monthly income = 36,000 / 12 = 3,000
Maximum payment = .28(3,000) = 840
PV = 840[1 – 1/1.005360] / .005 = 140,105 Total Price Closing costs = .04(140,105) = 5,604
Down payment = 20,000 – 5604 = 14,396
Total Price = 14...

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