Stacy Picone is an aggressive bond trader who likes to speculate on interest rate swings. Market interest rates are currently at 9%, but she expects them to fall to 7% within a year. As a result, Stacy is thinking about buying either a 25-year, zero-coupon bond or a 20-year, 7.5% bond. (Both bonds have $1,000 par values and carry the same agency rating.) Assuming that Stacy wants to maximize capital gains, which of the two issues should she select? What if she wants to maximize the total return (interest income and capital gains) from her investment? Why did one issue provide better capital gains than the other? Based on the duration of each bond, which one should be more price volatile?

the answer from my teacher:

my question: I don't understand how she calculated the PVIFA_{9%, 20 yrs,} PVIFA_{9%, 25 yrs , and} PVIFA_{7%,24 yrs in this answer. could you help me to figure it out?}

Current price of the bonds at 9% market interest: Zero-coupon bond: Price=$1,000PVIFA9%,25yrs.+$1,000.116=$116 7.5%,20-year bond (assume annual payments): Price=$75PVIFA9%,20yrs.+$1,000PVIFA9%,20yrs.=$759.129+$1,000.178=$862.68 Prices based on 7% rate in one year: Zero-coupon bond: Price=$1,000PVIFA7%,24yrs.+$1,000.197=$197 7.5\%, 19-year bond (assume annual payments): Price=$75PVIFA7%,19yrs.$1,000PVIFA7%,19yrs.=$7510.336+$1,000.277=$1,052.20 Capital gains: Zero-coupon bond: Gain =$197$116=$81 7.5\% bond: Gain =$1,052.20862.68=$189.52 To maximize capital gains per bond, buy the 7.5%,20-year bond; but this doesn't take into account he big difference in the amount (cost) invested. To do that, we should compare holding period returns: HPR=PurchasepriceInterest+CapitalgainsZero-couponbond:7.5%bond:HPR=$116$81=69.8%HPR=$862.68$75+$189.52=30.7%