Back to the Story of Lanna Loaner

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 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.

2. 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)

3. 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). 0 1 2 3 4 5 6 7 8 9 10

4. What I already Know If I sweep all that money the bank loaned forward to year 5, it is equal to the bank having $51,596 dollars out on loans. 0 1 2 3 4 5 6 7 8 9 10

5. New Picture I have to get my banker paid back over a period of 60 equal payments with 8% interest compounding monthly. 5y 1m ---------------------------------------------------------------- 10y 5 -$51,956

6. 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.

7. 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.

8. 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

9. 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

10. 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”!

11. 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

12. 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

13. Turning on our Sweeper $51,956 * 0.0202783 = $1046.28/month 5y 1m ---------------------------------------------------------------- 10y 5 -$51,956

14. 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