back to the story of lanna loaner lanna loaner has just graduated from college with a debt of...
DESCRIPTION
Drawing Pretty Pictures This time I’m going to sweep all the money into a pot at year #5. (Partially because I’ve already done half the problem and I’m lazy).TRANSCRIPT
![Page 1: Back to the Story of Lanna Loaner Lanna Loaner has just graduated from College with a debt of $51,596 Of course student loan programs don’t expect Lanna](https://reader036.vdocuments.us/reader036/viewer/2022083119/5a4d1ad67f8b9ab059973479/html5/thumbnails/1.jpg)
Back to the Story of Lanna Loaner
• Lanna Loaner has just graduated from College with a debt of $51,596
• Of course student loan programs don’t expect Lanna to pay off her loan on graduation day.– They’ll have her pay it off over the next say 5
years in monthly installments– Lets also say the interest rate changes to 8% with
monthly compounding.
![Page 2: Back to the Story of Lanna Loaner Lanna Loaner has just graduated from College with a debt of $51,596 Of course student loan programs don’t expect Lanna](https://reader036.vdocuments.us/reader036/viewer/2022083119/5a4d1ad67f8b9ab059973479/html5/thumbnails/2.jpg)
Step #1 in Problem Solving
• Let pick the perspective for the story problem. (We have the bank that has money loaned out and is going to collect payments - or we have Lanna).
• This time I’m going to pick the banks perspective (I could make it work either way)
![Page 3: Back to the Story of Lanna Loaner Lanna Loaner has just graduated from College with a debt of $51,596 Of course student loan programs don’t expect Lanna](https://reader036.vdocuments.us/reader036/viewer/2022083119/5a4d1ad67f8b9ab059973479/html5/thumbnails/3.jpg)
Drawing Pretty Pictures
0 1 2 3 4
5 6 7 8 9 10
This time I’m going to sweep all the money into a potat year #5. (Partially because I’ve already done half theproblem and I’m lazy).
![Page 4: Back to the Story of Lanna Loaner Lanna Loaner has just graduated from College with a debt of $51,596 Of course student loan programs don’t expect Lanna](https://reader036.vdocuments.us/reader036/viewer/2022083119/5a4d1ad67f8b9ab059973479/html5/thumbnails/4.jpg)
What I already Know
0 1 2 3 4
5 6 7 8 9 10
If I sweep all that money the bank loaned forwardto year 5, it is equal to the bank having $51,596 dollarsout on loans.
![Page 5: Back to the Story of Lanna Loaner Lanna Loaner has just graduated from College with a debt of $51,596 Of course student loan programs don’t expect Lanna](https://reader036.vdocuments.us/reader036/viewer/2022083119/5a4d1ad67f8b9ab059973479/html5/thumbnails/5.jpg)
New Picture
55y 1m ---------------------------------------------------------------- 10y
-$51,956
I have to get my banker paid back over a period of 60 equalpayments with 8% interest compounding monthly.
![Page 6: Back to the Story of Lanna Loaner Lanna Loaner has just graduated from College with a debt of $51,596 Of course student loan programs don’t expect Lanna](https://reader036.vdocuments.us/reader036/viewer/2022083119/5a4d1ad67f8b9ab059973479/html5/thumbnails/6.jpg)
Magic Number Come Out and Play
• I need magic number that will sweep these future payments of unknown size, back into my money pot.
• Two Observations• I have 60 numbers to be swept back - if I have
to do 60 P/F magic numbers I’m going to puke• I don’t know how big these 60 numbers are.
![Page 7: Back to the Story of Lanna Loaner Lanna Loaner has just graduated from College with a debt of $51,596 Of course student loan programs don’t expect Lanna](https://reader036.vdocuments.us/reader036/viewer/2022083119/5a4d1ad67f8b9ab059973479/html5/thumbnails/7.jpg)
Equal Payments Have a Special Name
• Annuity• An annuity is a series of equal payments• Common occurrences of this type of cash
flow– Mortgage Payments– Payments out of Retirement Funds– Engineers projecting the same earnings from
their project year after year.
![Page 8: Back to the Story of Lanna Loaner Lanna Loaner has just graduated from College with a debt of $51,596 Of course student loan programs don’t expect Lanna](https://reader036.vdocuments.us/reader036/viewer/2022083119/5a4d1ad67f8b9ab059973479/html5/thumbnails/8.jpg)
Enter a New Super Hero
• A/P• A/P stands for an Annuity
– who's Present Value• A/P * Present Value =
– An Annuity with the same– total value
![Page 9: Back to the Story of Lanna Loaner Lanna Loaner has just graduated from College with a debt of $51,596 Of course student loan programs don’t expect Lanna](https://reader036.vdocuments.us/reader036/viewer/2022083119/5a4d1ad67f8b9ab059973479/html5/thumbnails/9.jpg)
What do I know
• I know I have a banker who is out $51,596.• How much money do I have to sweep back
into his pot before he is going to be happy?• Because I’m not paying him off on graduation
day - I’ll have to sweep the money back with interest
• I have a present value– $51,596 * A/P = size of those annuity payments
![Page 10: Back to the Story of Lanna Loaner Lanna Loaner has just graduated from College with a debt of $51,596 Of course student loan programs don’t expect Lanna](https://reader036.vdocuments.us/reader036/viewer/2022083119/5a4d1ad67f8b9ab059973479/html5/thumbnails/10.jpg)
OK, Now I Have Everything but the Stupid Formula for A/P
• A/P i, n = {( i * [ 1 + i ] n)/( [ 1 + i ]n - 1) }• This sounds like a formula to put in a spread
sheet or to save in a calculator so that nimble fingers can’t punch it in wrong
• I didn’t do a derivation of the formula• Thing I remember most about that derivation was
that I never wanted to see it again• Look at the Formula and Say “I Believe”!
![Page 11: Back to the Story of Lanna Loaner Lanna Loaner has just graduated from College with a debt of $51,596 Of course student loan programs don’t expect Lanna](https://reader036.vdocuments.us/reader036/viewer/2022083119/5a4d1ad67f8b9ab059973479/html5/thumbnails/11.jpg)
Ok - It’s a really cool formula but what does it all mean
• i is the interest rate– Oh that’s not so bad– We know the interest rate will be 8% per year after her
graduation BUT• We ALSO know that after she graduates the
banker is going to ream her one - its compounding monthly– 8%/12 months/year = .667%/month– i is equal to 0.00667
![Page 12: Back to the Story of Lanna Loaner Lanna Loaner has just graduated from College with a debt of $51,596 Of course student loan programs don’t expect Lanna](https://reader036.vdocuments.us/reader036/viewer/2022083119/5a4d1ad67f8b9ab059973479/html5/thumbnails/12.jpg)
More Coolness with the Formula
• n is the number of payments and– the number of compounding periods
• In this case Lanna will make– monthly payments for 5 years or– 60 payments
• n = 60• Plug and Crank
– A/P i, n = {( 0.00667 * [ 1 + 0.00667 ] 60)/( [ 1 + 0.00667 ] 60 - 1) } = 0.0202783
![Page 13: Back to the Story of Lanna Loaner Lanna Loaner has just graduated from College with a debt of $51,596 Of course student loan programs don’t expect Lanna](https://reader036.vdocuments.us/reader036/viewer/2022083119/5a4d1ad67f8b9ab059973479/html5/thumbnails/13.jpg)
Turning on our Sweeper
55y 1m ---------------------------------------------------------------- 10y
-$51,956
$51,956 * 0.0202783 = $1046.28/month
![Page 14: Back to the Story of Lanna Loaner Lanna Loaner has just graduated from College with a debt of $51,596 Of course student loan programs don’t expect Lanna](https://reader036.vdocuments.us/reader036/viewer/2022083119/5a4d1ad67f8b9ab059973479/html5/thumbnails/14.jpg)
Observations About A/P
• A/P is sometimes called a capital recovery factor
• In many problems you will have an initial capital outlay.– If you multiply this initial outlay by the A/P
factor it tells you how big the payments will have to be starting with the next compounding period to pay back the capital