SOLUTION: Ok I have a problem that I believe I solved but I just want to be sure I am completing it correct. So here is the problem Zero coupon bonds do not yield periodic interest. Inst

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Question 430363: Ok I have a problem that I believe I solved but I just want to be sure I am completing it correct. So here is the problem
Zero coupon bonds do not yield periodic interest. Instead the purchaser buys the bond for less then the face value and then is paid full face value when the bond is mature. Before the bond is matures, its market value(price paid by a purchaser in the bond market) is determined by the prevailing market interest rate.
Below consider a 15 year bond with a face value of $1000
A) Determine the current market value of the bond if the prevailing market interest rate is 5% per year.
B) Determine the prevailing market interest rate if the correct market value of the bond is $300

So this is how I approached part A
Current value = 1000
Initial value = X
Rate 5%
Time = 15 years
term = 1
So 1000=x(1+(0.05/1))^15
Which comes out to $481.01
Is this correct? Buying a bond for approx. half value seems logical.

For Part B I approached it the following way.
Current value=1000
Initial value=300
rate = x
time = 15 years

1000=300e^r(15)
solved for r getting 8.02% This seems logical as a higher rate would mean a lower initial value
I am new to these problems so just want to be sure I am approaching them correctly. Thank you in advance for your help.

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Question: In Part A you are using compounding
at one-year intervals.
In Part B you are using continuous compounding.
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The work is correct for both but why do you
change from one compounding to the other?
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Cheers,
Stan H.