reinvestment income to realize YTM

A 5 year 9% semiannual-pay bond priced with a YTM of 8%, par value 100,000 What is dollar amount of reinvestment income that must be earned on each bond if it is held to maturity and the investor is to realize the current YTM? Solution says (1.04^10)(104,055.45) - 100,000 - 10(4500) = \$9,027.49. I understand that the calculated PV must be 104,055.45 but don’t know why it is multiplied by (1.04^10) or why the par value and coupon amount is being subtracted. Can someone please explain? Thanks.

Today you have a bond whose PV = 104055.45 In the future 5 years later (10 semi-annual periods) later - you would payback 100000 (Par value) Also over the course of the 10 periods - you paid coupons of 4500. Now if you had reinvested the 104055.45 at the 4% rate of interest for the 10 periods, how much would you get back? That is your reinvestment income. and you thus get back your YTM. Hope this helps.

Yes it does. Thank you for the explanation!

How do you get 104055.45 value??? Thank you

Method 1: bond functions 2nd Bond SDT=1.0100 (1-01-2000) Down CPN=9 Down RDT=1.0105 (1-01-2005) Down ACT Down 2/Y Down YLD=8 PRI --> CPT 104.0554475 The Bond function assumes a 100 Par value. Since Par of the above bond is 100000 -> multiply by 1000 to get 104055.45 Method 2: TVM functions N=10 I/Y=4 PMT=4500 FV=100000 CPT PV = 104055.45