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Finding present value

  1. Nov 5, 2008 #1
    1. The problem statement, all variables and given/known data
    A $50 U.S. Savings Bond paying 6.22% compounded monthly matures in 11 years 2 months. What is the present value of the bond?


    2. Relevant equations



    3. The attempt at a solution
    I ended up getting $50.95
     
  2. jcsd
  3. Nov 6, 2008 #2

    Mark44

    Staff: Mentor

    That's not a reasonable answer. No reasonable person would pay $50.95 now for a bond whose value is $50 at maturity, which is 11 years 2 months in the future.

    The idea is that you pay a smaller value in the present and get a larger value in the future. Surely you must have an equation that you can use.
     
  4. Nov 6, 2008 #3
    The compound interest formula?
     
  5. Nov 6, 2008 #4

    Mark44

    Staff: Mentor

    Sure. Give it a whirl and show us your work.
     
  6. Nov 6, 2008 #5
    I did 50(1+(0.0622/12))^(12/11.167) so...is the answer $99.96?
     
  7. Nov 6, 2008 #6

    HallsofIvy

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    You are going the wrong way! That would be the return if you invested $50. With a $50 bond,you get $50 on maturity. How much would invest (the principal) at 6.22% interest, for 11 years 2 months, to get a return of $50? (it will be less than $50.)

    Also the number of months in 11 years 2 months is 11.167 times 12, not divided by 12.
     
  8. Nov 6, 2008 #7

    symbolipoint

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    Try going to a lower level. You know the compounding is monthly; so how many months does the bond earn? This is 6.22 % each month; and the interest is COMPOUNDED monthly.
     
  9. Nov 6, 2008 #8

    HallsofIvy

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    No, the interest is NOT 6.22% each month. The problems says "A $50 U.S. Savings Bond paying 6.22% compounded monthly". While it is compounded monthly, the interest rate stated is, as always, annual interest.

    Even the United States Government isn't stupid enough to pay 12(6.22)= 74.64% annually!
     
  10. Nov 6, 2008 #9
    My bad...I did 50/(1+(0.0622/12))^(-12x11.167). That how I ended up with 99.96.
     
  11. Nov 6, 2008 #10
    Is it 99.96 or not?
     
  12. Nov 6, 2008 #11

    Mark44

    Staff: Mentor

    NOT. Please reread (or maybe read) what Halls and I have written. It should be a clue when you ask whether $99.96 is correct and someone replies that you're going the wrong way.
     
  13. Nov 6, 2008 #12
    I used the compound interest formula and ended up with that so what did I do WRONG?
     
  14. Nov 7, 2008 #13

    Mark44

    Staff: Mentor

    Carefully read Halls's post #6.
     
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