Calculating the Price of a Bond

Question

Would someone be able to help me understand if I am doing this calculation for some homework correctly? I know I could do it on my calculator, but I'm trying to understand the process behind it as well.

A 12 year, 7.1%, $1,000 bond that pays interest semiannually is presently selling with an Yield-to-maturity (YTM) of 5.7%. What is the price of the bond, and what kind of bond is this?

= (35.5/1.0285) + (35.5/1.0285^2) + (35.5/1.0285^3) + (35.5/1.0285^4) + (35.5/1.0285^5) + (35.5/1.0285^6) + (35.5/1.0285^7) + (35.5/1.0285^8) + (35.5/1.0285^9) + (35.5/1.0285^10) + (35.5/1.0285^11) + (1035.5/1.0285^1212)

= $1,070.31

Premium bond: Sells above face value (YTM < Coupon Rate on the bond)

Answer 1

You seem to be proceeding correctly: taking all the future cash flows back to the reference date (apparently the day of issue). You have correctly found the size of the coupon payment.

However....

This is a 12-year bond with semi-annual coupons. You need to continue the pattern in your suggested answer for 12 more terms to cover the 24 coupons on the bond. A formula approach is looking better, right?

And naturally, the maturity value is similarly discounted incorrectly. When you expend the coupons to 24 periods, the maturity value will be added to the last coupon.

Finally, there's a slight problem with the interest rate you're using to discount the payments. If the question said that the YTM was 5.7%, compounded semi-annually, then your calculation is correct, using half of the 5.7%. If 5.7% is the effective annual rate, then you should find the discount rate by taking the square root of (1.057). Exact terminology varies from jurisdiction to jurisdiction...