Please help! ROI VS YTM!?

The question is "If you purchase a 100$ bond. At a 5% discount to par value. The bond's coupon rate is 8% and matures in 5 years. What is the the bond's approximate yield to maturity?"

I thought of calculating the profit which in this case would be 40$ (8$ per year*5 years+5$ profit as we bought the bond at 95$) and dividing that by my initial investment. So do 40$/95$ which gives me like 40%. 

But this seems to be the ROI and not the yield the maturity. 

I have found a pretty complicated formula for YTM=(Annual interest+(Redemption Value-Bond Price)/#Years to Maturity)/(Redemption Value+Bond Price)/"). 

1)How would you find the YTM easily and fast? Cuz in an interview I guess I won't have the time to use this whole formula. 

2)Why YTM differs from the ROI?

Comments (5)

Jan 22, 2021 - 4:59pm

1) How would you find the YTM easily and fast? Cuz in an interview I guess I won't have the time to use this whole formula. - Don't think I have actually be asked to calculate YTM in an interview. Usually just general questions about the YTM compared to other rates.  

2).  YTM is rate used to calculate NPV of 0 where ROI is more of an output from the purchase.  

Jan 22, 2021 - 7:14pm

If they want you to calc it then they will give you enough time.  The formula above is not that hard but if you can't remember that I would recommend remembering the relationships between NY,CY, YTC, YTM. 

YTM=(Annual interest+(Redemption Value-Bond Price)/#Years to Maturity)/(Redemption Value+Bond Price)

Also equals YTM= (annual interest plus or minus Premium or discount)/ Years / ( FV plus or minus Premium or discount)/2

Jan 23, 2021 - 2:25am

Got it. Thank you very much bro. I have another little question. Can you please help me?

The question is: How do increase/decrease in interest rates affect options prices?

I figured that any change in interest rates , affect supply and demand, and that obviously would affect options prices. 

High interest rates would imply lower option prices. 

Low interest rates would imply higher option prices. For the law of supply and demand. 

Is this correct? Otherwise, how does it work in detail?

Jan 25, 2021 - 10:37am

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