Which $1000 bond has the higher YTM, a 20 yr bond selling for $800 current yield of 15% or 1 yr bond at 5%?

Question

what formula do i use? The one year bond is also selling for $800 with a current yield of 5%.

Answer 1

Supposing you spend $800 on each bond.

After 20 years, bond A becomes 800x 1.15^20 + 200 =13,293

Bond B becomes 800 x 1.05^20 = 2,123

Clearly bond A is far better.

Answer 2

this largely depends on if those percentages are the nominal yield or the redemption yield.

I.E. is the 15% and 5% representative of how much you'll get back when it expires, or how much you get back per year.

if it's per year, obviously 15% for 20 years is far better than 20 x 5% in 1 year slots.

though of course, rates change, and if economic conditions become such that the 1 year balloons to 16%, you lose out... though the market value of the bond means it can be redeemed progressively so you can of course make moves to prevent such things as they draw close.