CFA CFA Level 1 Calculations

# Calculations

• Author
Posts
• thomas111121
Participant
• CFA Level 1
1

Can anyone tell me how to go about calculating the following equation. It doesn’t show it step-by-step in the book

1 2 3
E.G. If 102.960 = 5/(1+r) + 5/(1+r) + 105(1+r) , r = 0.03935

How do you come to the answer r=0.03935?

Thanks

• simply_complex2
Participant
• CFA Level 1
5

@thomas111121â€Œ what is the original question and what calculator do you use? i wouldn’t algebraically solve the equation since it would be time consuming. i would use the TVM function on your calculator. based on the info you posted N=3, PV=102.96, FV=100, PMT=5, compute I/Y. you can also just guess and check based on the answer choices but that would take more time.

hope that helps!

• thomas111121
Participant
• CFA Level 1
5

the question is in relation to pricing bonds. Suppose that the one year spot rate is 2%, the 2 year spot rate is 3% and the 3 year spot rate is 4%. Calculate the price of the 3 year bond that makes a 5% annual coupon payment which comes to 102.960. The problem is how do I calculate the YTM? I know you put the 102.960 = 5/(1+r) + 5/(1+r)squared + 105(1+r) cubed to work it out but I don’t know how to compute it. I have a texas B11 Plus professional

• thomas111121
Participant
• CFA Level 1
3

you’re a star ðŸ™‚

• simply_complex2
Participant
• CFA Level 1
2

so in this case you actually don’t need the spot rates the question provides you with (you would plug in the spot rates to calculate the PV of the bond using the arbitrage free valuation approach.) you have the right formula listed above to calculate YTM, but you actually don’t need to go through all of that math since you can just use the time value of money function on your calculator (its the thirds row down from the top of the calculator). the question gives you the present value (-102.96), future value (100), coupon payment (5% * 100) and periods to maturity (3) using these inputs you can press the CPT (compute) I/Y to get the yield to maturity. this will solve for r in the formula you posted above above

to use the TVM function your going to input the number first and then press the respective button (input-102.96, press PV, input 3 press N)

hope this cleared things up a bit! if not ask away and i can try to clarify or someone else may be able to help ðŸ™‚