Zero Coupon Bonds?

[Happydesta]

I have been trying to figure out what formula to use for this question for days.

NIkky purchased a zero coupon bond for 35559.45. The bond matures in 10 years and has a face value of 45,000. Find the effective rate of interest if the bond is compounded semiannually.

I thought I would try to use a compounding formula to first find out the interest rate but haven't been able to get that.

Thanks for any help!

 

[Denis]

I have been trying to figure out what formula to use for this question for days.

NIkky purchased a zero coupon bond for 35559.45. The bond matures in 10 years and has a face value of 45,000. Find the effective rate of interest if the bond is compounded semiannually.

I thought I would try to use a compounding formula to first find out the interest rate but haven't been able to get that.

Thanks for any help!

35559.45 (1 + r)^20 = 45000

Solve for r, which is the semiannual rate.
Convert that to annual.

 

[Happydesta]

This is what I have got so far. I am really stumped and can't remember how to solve. I missed a class period in weekend college that is the same as a whole week.

35559.45 (1+r)^20=45,000
-35559.45
(1+r)^20=9440.55
1+r^20=9439.55

I don't know where to go from here or even if this is correct?

 

[Denis]

35559.45 (1+r)^20 = 45000

Don't let the "looks" of that equation scare you: same as ab = c

Rule: if ab = c, then b = c / a ; so:
(1+r)^20 = 45000 / 35559.45 .....OK?

Rule: if a^b = c, then a = c^(1 / b) ; so:
1+r = (45000 / 35559.45)^(1/20)
r = (45000 / 35559.45)^(1/20) - 1 .....OK?

Go get your calculator :idea: