# Finding present value

1. Nov 5, 2008

### DCHomage

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. Nov 6, 2008

### 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.

3. Nov 6, 2008

### DCHomage

The compound interest formula?

4. Nov 6, 2008

### Staff: Mentor

Sure. Give it a whirl and show us your work.

5. Nov 6, 2008

I did 50(1+(0.0622/12))^(12/11.167) so...is the answer $99.96? 6. Nov 6, 2008 ### HallsofIvy Staff Emeritus 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.

7. Nov 6, 2008

### symbolipoint

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.

8. Nov 6, 2008

### HallsofIvy

Staff Emeritus
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! 9. Nov 6, 2008 ### DCHomage My bad...I did 50/(1+(0.0622/12))^(-12x11.167). That how I ended up with 99.96. 10. Nov 6, 2008 ### DCHomage Is it 99.96 or not? 11. Nov 6, 2008 ### 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.

12. Nov 6, 2008

### DCHomage

I used the compound interest formula and ended up with that so what did I do WRONG?

13. Nov 7, 2008