1. Our First Magic Number F/P i,n Formula is (1 + i) n The effect of F/P is to take a present number of dollars and move them n compounding periods into the future at a rate of return (or interest rate) of i F/P * Present Value = Future Value

2. Example of Use Lanna Loaner is using student loans to finance the cost of her college education. Lanna figures she will take 5 years to graduate. She figures that she will take 12 hours each semester (except summer). –Lanna figures each semester will cost $1,820 in tuition and fees –Lanna expect to spend $500/semester in books and supplies

3. Lanna’s Learning Legend Lanna figures she will spend $475/month on university housing (for 9 months of the year - she’ll live at home and work during the summers). Lanna figures she will need $400/month for food and clothing Lanna figures she can save $5,000 each summer from working.

4. Lanna Loves Learning Lanna arranges to get student loans sponsored by the government Future Income Tax Enhancement Agency. The loans will be made yearly with interest a 6% compounded annually. How much debt will Lanna accumulate by the time she graduates?

5. Step #1 Turn the story problem into a cash flow. Figure out what Lanna needs in loans every year –2 semesters tuition and fees $1820 * 2 = $3640 –2 semesters books and supplies $500 * 2 = $1000 –9 months housing $475 * 9 = $4275 –9 months food and clothing $400 * 9 = $3600

6. Continuing Step #1 Total up Lanna’s expenses –$3640 + $1000 + $4275 + $3600 = $12,515 When Lanna starts college she probably won’t already have a pile of money saved, so she will have to take the full loan the first year - thereafter Credit Lanna’s earnings in the summer –$12,515 - $5000 = $7,515

7. Making my Cash Flow First decision - Who’s perspective will I take (I have Lanna taking the loan and the bank giving it out). I’m going to take Lanna’s At the beginning of each school year Lanna sees money moving into her pocket –We use the convention that money moving in our pocket is positive - money moving out is negative.

8. Drawing a Pretty Picture $12,515 $7,515 0 1 2 3 4 5 - Lanna Gets Her Diploma How Big a Hole will Lanna be in?

9. Going to the Next Step Using magic numbers to “sweep up” all the money into one pile I’m will use F/P magic number because I want to sweep dollars from the present into one pile in the future

10. Apply F/P Magic Numbers 0 1 2 3 4 5 - Lanna Gets Her Diploma $12,515 We need to sweep this number ahead 5 interest periods into the pot of money Lanna will owe

11. Pick Out the Number to Use I need an F/P magic number because I have a present dollar amount I want to sweep into the future pot. I need it to be an F/P i, 5 because I want to sweep 5 compounding periods into the future I need it to be an F/P 6, 5 because my interest rate each year is 6%

12. Apply the formula to get my Magic Number (1 + 0.06) 5 = 1.33823 The formula I used is (1 + i ) n

13. Moving Along to My Next Number 0 1 2 3 4 5 - Lanna Gets Her Diploma $12,515 * 1.33823 $7,515 I now want to sweep this money into the future pot. F/P Magic number needed I need to move 4 compounding periods I need 6 % interest

14. Calculate My Magic Number (1 + 0.06 ) 4 = 1.26248 Note that this number is smaller than 1.33823 Reality Check - Does it make sense that if money doesn’t have as long to earn interest that it will earn less interest? –Yes so we’re probably still on the right track

15. Next Number 0 1 2 3 4 5 - Lanna Gets Her Diploma $12,515 * 1.33823 $7,515 * 1.26248 I need to sweep this number 3 compounding periods into the future. How many periods do I need to sweep this one and this one

16. Now for the Last Step 0 1 2 3 4 5 - Lanna Gets Her Diploma $12,515 * 1.33823 $7,515 * 1.26248 $7,515 * 1.19102 $7,515 * 1.1236 $7,515 * 1.06 Now we will add up all the numbers to sweep them into the pot.

17. Adding Up the Numbers $12,515 * 1.33823 = $16,748 –$7,515 * 1.26248 = $9,488 –$7,515 * 1.19102 = $8,950 –$7,515 * 1.1236 = $8,444 –$7,515 * 1.06 = $7,966 Total swept into the future debt pot is –$51,596