Question on Bond Valuation?

Question

I don't get the difference between the effective annual interest rate and nominal rate, how does it make the answer for this question any different??
the question is: you are considering a 10 year 1,000 par value bond. its coupon rate is 9 percent, and interest is paid semi-annually. If you require an "effective" annual interest rate (not a nominal rate) of 8.16 percent, then how much should you be willing to pay for the bond?
I used a financial calculator to do the following:
since its semi-annual i calculated payment as (PMT): .09/2 x 1000 = 45
Number of years (N) = 10 x 2 = 20
Interest (I/Y) = 8.16/2 = 4.08
Future Value (FV) = 1000
and i computed PV which equals = 1,056.68
PV is max price investor is willing to pay for the bond, did i get it right, and how is effective vs. nominal interest rate make my answer any different? rather, what does it even mean?

Answer 1

The nominal rate is if it was at par, either when it was purchased or if you purchased it at $1000. However, since you only require 8.16% per year instead of 9%, paying 1056.68 would be the equivalent contract in terms of cash flows, but offered at the lower rate. You did make a calculation error however. 4% per half year is the same thing as 8.16% annually due to compounding. You need to slightly alter your rate in I/Y to 4%.

So, the effective rate has precisely the same cash flows, except the initial amount loaned.

Answer 2

imagine of how a lot you may ought to deposit in a coupon rates account that paid 6.2% in line with annum as a thanks to make each of the coupon funds and the basically top face fee of the bond. For the first annual coupon which for a $a million,000 face fee bond could be 0.07 * $a million,000 or $70, you may ought to maintain $70 / a million.062. in addition each of the coupons, could require you to maintain $70 / a million,062^t the position t is the type of years till the coupon, then there is the face fee itself and also you may ought to maintain $a million,000 / a million.062^9 for that volume. for this reason you've: PV = $70 / a million.062 + $70 / a million.062^2 + $70 / a million.062^3 + ... + $70 / a million.062^9 + $a million,000 / a million.062^9 be conscious that each of the coupon funds are a summation of a finite geometric series so instead of doing each of the calculations, you are able to do exactly a summation of a finite geometric series calculation for this reason you've: PV = $70 * ( ( a million - a million / a million.062^10 ) / ( a million - a million / a million.062 ) - a million ) + $a million,000 / a million.062^9 .: PV = $a million,053.ninety 4 for this reason the $a million,000 face fee bond with 7% annual coupons and 9 years left to adulthood could provide the investor 6.2% in line with annum returns if offered for $a million,053.ninety 4. in addition, in case you had deposited $a million,053.ninety 4 in a coupon rates account that paid 6.2% in line with annum, you are able to withdraw $70 on the proper of each three hundred and sixty 5 days and yet another $a million,000 on the proper of the 9 years it truly is why the marketplace fee of the bond could be priced as such.