Notes for April 21, 22: Buying and financing a new car

Page 36:   Christina is trying to buy a car for $23,599.

Finance Option 1 (#1-2 on page 36) is a 3 year loan at 5.99% with 10% down payment.

Down payment is 10%. 10% = 0.10.  0.10*23599 = $2359.90

Loan amount = 23599 - 2359.9 = $21239.10
                            OR, 0.9*23599 = $21239.10.  Either way is the same answer.
                            The LOAN AMOUNT goes in the Finance App as "PV"

N = 3*12
I% = 5.99
PV = 21239.10
PMT = X
FV = 0
P/Y = 12
C/Y = 12
END

Using the Finance App, her payment would be $646.04

Question 2:  Depreciation. After 3 years, the car is worth only $14,250.

Total cost of car:  N*PMT + Down Payment - Value of car at payoff (when loan is paid)

3*12*646.04 + 2359.9 = $25,617.34

At the end of the 3 years, the car is worth (can be sold for) $14,250.

$25617.34 - $14250 = $11,367.34

 Finance Option 2 (#3 on page 36) is a 0% down and 0% APR for two years.

N = 2*12
I% = 0
PV = 23599
PMT = X
FV = 0
P/Y = 12
C/Y = 12
END

Under these conditions, her monthly payment would be $983.29.

Total Cost = 2*12*983.29 + 0 - value of car at 2 years

                 = $23,598.96 - $17,629  (given in the packet) = $5969.96.

Christina should take option 2, IF SHE CAN AFFORD IT, because the total cost is about 1/2 of option 1. But, it is a very high monthly payment, which many people can't afford.

Finance Option 3 (#4-5 on pages 36-37) is a LEASE at $349 per month with a BALLOON PAYMENT of $1200 at the end of 3 years.

In a lease, you DO NOT own the car at the end! It's basically a long-term rental.

Total Cost = 3*12*349 + 1200 = $13,764

Question 5: Is she being charged interest?

N = 3*12
I% = X
PV = 23599
PMT = -349
FV = -14250  (value of the car after 3 years, which is given in #2 on page 36)
P/Y = 12
C/Y = 12
END

From the Finance App, I% = 5.586%  (not even including the balloon payment at the end).

Should she take it? Maybe, if that's the only way she can afford to have a car. But there's no long-term payoff - you don't own the car at the end, so the total cost is the highest.

Option 4: (#6 on page 37)  Lease to purchase (a LEASE, but with the option to buy at the end). APR = 1.9%, 3 years. At the end, she can pay the depreciated value, or walk away for a fee of $150.

N = 3*12I% = 1.9
PV = 23599
PMT = X
FV = -14250
P/Y = 12
C/Y = 12
END

Payment = $289.93 each month.

Total Cost = 3*12*289.93 = $10,437.48

Now, either she walks away: $10437.48 + 150 = $10,587.48 total cost (and no car!), OR

She pays for the depreciated value: 
10,437.48 + 14250 (she pays) - 14250 (because she keeps the car) = $10,437 total cost.

New Homework:

You were already responsible for pages 40, 41, and 42. Now, you also need to complete pages 43 and 44. Turn in all 5 pages next time.

Notes from April 19, 20th: Amortization (paying off depts) AND HOMEWORK HINTS!!!

Amortization starts on page 35 in your packet:

1. AMORTIZATION TABLE

An amortization table takes a payment and splits it into the part that pays off (part of) the principal and the part that pays the interest.

Interest payments help the company, NOT YOU. You want to pay as much toward the PRINCIPAL as possible. The interest will be taken out FIRST.

TABLE for JR's amortization (We are only doing 11 months, not 36!!!) :

JR owes $3000, with an 16.8% Annual Percentage Rate.
He will pay $319.97 per month

16.8% APR / 12 months = 1.4% per month = 0.014

Month   Balance            Interest Paid                  Principal Paid                   New Balance
1            $3000              3000*.014= $42            319.97-42 =$277.97          3000-277.97    =$2722.03
2            $2722.03          *.014 = $38.11             319.97-38.11=$281.86      2722.03-281.86=$2440.17
3            $2440.17          *.014 = $34.16             319.97-34.16=$285.81     2440.17-285.81=$2154.36
4            $2154.36          *.014 = $30.16             319.97-30.16=$289.81     2154.36-289.81=$1864.55
5            $1864.55          *.014 = $26.10             319.97-26.10=$293.87     1864.55-293.87=$1570.68
6            $1570.68          *.014 = $21.99             319.97-21.99=$297.98     1570.68-297.98=$1272.70
7            $1272.70          *.014 = $17.82             319.97-17.82=$302.15     1272.70-302.15=$970.55
8            $970.55            *.014 = $13.59             319.97-13.59=$306.38     970.55-306.38  =$664.17
9            $664.17            *.014 = $9.30               319.97-9.30  =$310.67     664.17-310.67  =$353.50
10          $353.50            *.014 = $4.95               319.97-4.95  =$315.02     353.50-315.02  =$38.48
11          $38.48              *.014 = $0.54                                      $38.48                                   =$0

His last payment needs to be for $0.54 + $38.48 = $39.02.

FINANCE APP NOTES (this was on the board, not in the packet)
Pheonix has a balance of 6759, with an APR of 19.8%. She can pay $275 each month. How long will it take to pay it off?

N = X
I% = 19.8
PV = 6750  (not negative)
PMT = -275  (negative; it's coming out of her pocket)
FV = 0  (to pay off)
P/Y = 12 (always monthly for credit cards)
C/Y = 12
END

X = 31.73 months.  We must round UP, because 31 months is not enough.  X = 32 months

32/12 = 2.67 years (2 years, 8 months)

Hints for the Homework Assignment:

(1) Page 40 in your packet (should be already done)

       Part (a) is the long part.
       Step 1:  Look at the starting balance, and the list of transactions, and
                    find the balance after each transaction.
                   ***HINT*** If 2 or more transactions happen in the same day, do it all in one step.
       Step 2: Figure out how many days the balance stays at each $ amount.
                   ***HINT***  Your number of days should be: 1, 3, 3, 4, 4, 4, 3, 1, and 8.
       Step 3: Multiply each balance $ amount by the number of days.
       Step 4: Add up all the answers from Step 3.
       Step 5: Divide by the number of days in the month
                   ***HINT*** There are 31 days in March.
                   ***HINT*** Your final answer should be $28__.60 (I'm leaving two digits out)

        This is your AVERAGE DAILY BALANCE.

        Part (b):  ***HINT***  daily periodic rate = APR/number of days = 18.99/365
                      ***HINT***  Once you get your answer, change it to a decimal by dividing by 100.

        Part (c)
        Step 1: Get the finance charge
         ***HINT*** finance charge = (AVE DAILY BALANCE)(daily periodic rate)(number of days)
                                                        = (answer from part a)(answer from part b)(31)
        Step 2: Get the new balance
        ***HINT***  new balance = old balance + debits - credits + finance charge
                                                    = $2655.25+585.04-198.25+answer from step 1

        Part (d)
        ***HINT*** percentage paid = minimum payment / new balance * 100%
                                                              = 75/(answer to part c) * 100

(2) Page 41 in your packet

This is like the notes from today, above.
***HINT*** Start by applying sales tax to the price to get your starting balance:
                       799.99 + 0.0825*799.99 = $865.99
***HINT*** To get the old balance (for every month after 1), copy it from the previous new balance
***HINT*** The APR is 27.99. You need to divide that by 12 months and
                       convert to a decimal by dividing by 100. That gives you 0.023325.
                       To get the interest paid each month, multiply the OLD BALANCE by 0.023325.
***HINT*** To get the principal paid each month, subtract $80 - the interest paid.
***HINT*** To get the new balance each month, subtract OLD BALANCE - PRINCIPAL PAID

The first 3 rows should look like:
MONTH      BALANCE      INTEREST PAID     PRINCIPAL PAID     NEW BALANCE
1                  $865.99            $20.20                       $59.80                        $806.19
2                  $806.19            $18.80                       $61.20                        $744.99
3                  $744.99            $17.38                       $62.62                        $682.37

(3) On the blank page 42, use the finance app to solve #5 on page 35.

***HINT***  Use the finance app
***HINT***  N is always 12*2, since payments are monthly for 2 years
***HINT***  I% and PV are given in the bullet points of #5 on page 35
***HINT*** PMT is "X" - This is what you are trying to find.
***HINT*** FV should be 0, since you are trying to pay it off.
***HINT*** P/Y and C/Y are both 12 (monthly for all credit card problems)
***HINT*** you should make sure payments are set to "end".
***HINT*** Your 4 answers should be $3__.89, $4__.76, $8_.42, and $1__.52 (leaving out digits)

Notes from 4/15 and 4/18 (credit cards)

Here you go.  Remember to try page 40 in the packet for homework.

And, of course, you can't make .53965 of a monthly payment, so really she has to make 42 monthly payments (always round up to the next whole number of payments).

42 months / 12 months per year = 3 1/2 years.

Finances Unit, notes from 4/13 or 4/14 Annuities and Stocks and Bonds

Several people were out today, so I took notes for you.

Here you go. If you need a hard copy of the notes, let me know.

Also, some more quick definitions:

STOCK: an investment security that gives you ownership in a company.
BOND: a security in which you actually lend money to a company.

STOCKS are riskier than BONDS (more likely to make more $, but also more likely to lose $).
On average, BONDS return 5% of the investment.
On average, STOCKS return 10% of the investment.

Piecewise functions

I'm putting the notes from the last couple of classes on here, from the packet through page 30, and then how to put the piecewise functions in the calculator to graph them.

 

And PAGE 32:

Sine function ...

And another type of function. When something has a pattern that REPEATS, like the giant Ferris wheel we modeled in class, we call it a PERIODIC function. Some of the most well known of these are the trig functions, sine (SIN), cosine (COS), and tangent (TAN). Here's a little review:

 So, that Ferris wheel (the Singapore Flyer) :  We drew a picture to model the situation, and then used cosines to figure out the height off the ground each minute for the 30 minutes it takes to go around the circle once:

 You have to put your calculator in DEGREE mode (push the [MODE] button) before doing this!

 And then, the regression to a SINE function works just the same as to a linear, exponential, or logistic function:

(1) Put the data into L1 and L2 using [STAT] EDIT
(2) Get the regression equation (this time it's [STAT] CALC "C")
(3) Put the equation in using [Y=].
(4) Turn on the StatPlot using [2nd] [Y=] and adjust your [WINDOW]
(5) Graph

Special note: For some reason, even though you put the calculator in DEGREE mode earlier, the SINE regression doesn't use degrees, it uses RADIANS. So to make the graph match up right, switch the mode back to RADIAN.

If you take a look at all the options under [STAT] CALC, you'll see we've only done a few of the very many functions available for calculating regression equations.

Logistics ...

Okay, so we've done linear, and we've done exponential. But there are a lot more functions to consider.

For instance, sometimes things start off growing really fast like an exponential function, but then things happen to slow down the growth. We talked in class about how the flu spreads exponentially, but then slows down and levels off when people start taking medicine. This is called a LOGISTIC function.

Here's what it looks like in action (re-creation of the game we played in class, in case you missed it) - each turn, each person that is already sick picks a random person to get them sick. But when the numbers start repeating themselves, people can't get sick AGAIN, so the growth slows down.

0.

 1.

 2.

 3.

 a little while later ...

We can do a regression on this type of function, just like with linear or exponential. The calculator steps are:

(1) Put data in, with [STAT] EDIT
(2) [STAT] CALC "B" (LOGISTIC)
(3) Turn on the StatPlot ([2nd] [Y=]), set the [WINDOW], and type the regression into [Y=]
(4) Graph