**Unformatted text preview: **an annuity due
calculator,
Most problems are ordinary annuities 19 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 20 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 21 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 22 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 = 140,105 + 14,396 = 154,501 23 Annuities on the Spreadsheet Annuities
Example
Example The present value and future value
The formulas in a spreadsheet include a
place for annuity payments
place Click on the Excel icon to see an
Click
example
example 24 Quick Quiz – Part II You know the payment amount for a loan and
You
you want to know how much was borrowed.
Do you compute a present value or a future
value?
value?
You want to receive 5,000 per month in
You
retirement. If you can earn .75% per month
and you expect to need the income for 25
years, how much do you need to have in your
account at retirement?
account 25 Finding the Payment Suppose you want to borrow $20,000 for a new
Suppose
car. You can borrow at 8% per year,
compounded monthly (8/12 = .66667% per
month). If you take a 4 year loan, what is your
monthly payment?
monthly 20,000 = C[1 – 1 / 1.006666748] / .0066667
C = 488.26 26 Finding the Payment on a
Finding
Spreadsheet
Spreadsheet Another TVM formula that can be found in a
Another
spreadsheet is the payment formula
spreadsheet PMT(rate,nper,pv,fv)
The same sign convention holds as for the PV and
The
FV formulas
FV Click on the Excel icon for an example 27 Finding the Number of Payments
Finding
– Example 6.6
Example Start with the equation and remember your
Start
logs.
logs. 1,000 = 20(1 – 1/1.015t) / .015
.75 = 1 – 1 / 1.015t
1 / 1.015t = .25
1 / .25 = 1.015t
t = lln(1/.25) / ln(1.015) = 93.111 months = 7.76
n(1/.25)
years
years And this is only if you don’t charge anything
And
more on the card!
more
28 Finding the Number of Payments
Finding
– Another...

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