Help review AI bond analysis

joesxm3

Thinks s/he gets paid by the post
Joined
Apr 13, 2007
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I have been trying to figure out if it is worth cashing in some high interest I-Bonds maturing in 2030 that will make my taxable income huge that year. I decided to ask AI to help. Grok got an error. CoPilot in the Edge browser seemed to handle the question but I think it made a mistake.

I think it did not handle the compounding of interest in scenario 2 correctly because it should have subtracted the tax each year rather than at the end. Maybe I phrased the prompt poorly. I think the final amount for scenario 2 should be lower. Does this make sense?

Here is the prompt:

I have a tax deferred bond worth $23,000 including $18,000 of taxable interest and paying 4% interest per year compounded annually. The basis in this bond is $5000. This bond matures in 5 years and I will have to pay tax at the rate of 24%. If i cash this bond now and pay tax at the rate of 12% on the $18,000 of taxable income and invest the proceeds at a rate of 2% interest and pay tax on this interest each year at the rate of 22% per year. which scenario yields greater value after five years?

Here is the response:

Let’s break down both scenarios to determine which one yields greater value after five years.

Scenario 1: Hold the Bond Until Maturity​

  1. Current Value of Bond: $23,000
  2. Interest Rate: 4% compounded annually
  3. Tax Rate on Maturity: 24%
Future Value Calculation: [ FV = PV \times (1 + r)^n ] [ FV = 23,000 \times (1 + 0.04)^5 ] [ FV = 23,000 \times 1.21665 ] [ FV = 27,982.95 ]

Tax Calculation: [ \text{Taxable Interest} = 27,982.95 - 5,000 = 22,982.95 ] [ \text{Tax} = 22,982.95 \times 0.24 = 5,515.91 ]

Net Value: [ \text{Net Value} = 27,982.95 - 5,515.91 = 22,467.04 ]

Scenario 2: Cash the Bond Now and Reinvest​

  1. Current Value of Bond: $23,000
  2. Taxable Interest: $18,000
  3. Tax Rate on Cashing: 12%
  4. Reinvestment Rate: 2% compounded annually
  5. Tax Rate on Interest: 22%
Tax Calculation on Cashing: [ \text{Tax} = 18,000 \times 0.12 = 2,160 ]

Proceeds After Tax: [ \text{Proceeds} = 23,000 - 2,160 = 20,840 ]

Future Value Calculation: [ FV = PV \times (1 + r)^n ] [ FV = 20,840 \times (1 + 0.02)^5 ] [ FV = 20,840 \times 1.10408 ] [ FV = 22,999.47 ]

Tax on Interest Earned: [ \text{Interest Earned} = 22,999.47 - 20,840 = 2,159.47 ] [ \text{Tax} = 2,159.47 \times 0.22 = 475.08 ]

Net Value: [ \text{Net Value} = 22,999.47 - 475.08 = 22,524.39 ]

Comparison​

  • Scenario 1 (Hold the Bond): $22,467.04
  • Scenario 2 (Cash and Reinvest): $22,524.39
Conclusion: Cashing the bond now and reinvesting the proceeds at 2% interest yields a slightly higher value after five years.
 
I didn't analyze the answer but LLMs are notoriously bad at math. If you want to pose math problems, you should sign up for GPT and make sure you use the GPT o1 preview model. It is reputed to be far better at math than earlier models. Even with o1, the only way to check is to do the calculation yourself (and know enough of the relevant math to be sure you are correct).
 
I watched all-in podcast this morning and they were talking about how impressive chat gpt o1 was at analyzing a cap sheet. That got me interested. I will probably buy a chat gpt subscription so I can play with it and see what it is like.
 
I went ahead and posited your prompt to ChatGPT o1 Preview. Here is its response (unanalyzed by me). It does arrive at different numbers than you posted.

To determine which scenario yields the greater value after five years, we will compare the two options:
  1. Scenario 1: Cash the bond now and invest the proceeds.
    • You pay tax at 12% on the taxable interest ($18,000).
    • You invest the after-tax proceeds at 2% interest per year, paying 22% tax on the interest each year.
  2. Scenario 2: Hold the bond to maturity.
    • You pay 24% tax on the $18,000 taxable interest when the bond matures after five years.
Let's calculate each scenario step by step.

Scenario 1: Cash the Bond Now and Invest the Proceeds​

Step 1: Calculate the tax on the $18,000 of taxable interest.The taxable interest is $18,000, and the tax rate is 12%.
Tax=18,000×0.12=2,160\text{Tax} = 18,000 \times 0.12 = 2,160Tax=18,000×0.12=2,160
Step 2: Calculate the after-tax proceeds.After paying the $2,160 tax, you are left with:
After-tax proceeds=23,000−2,160=20,840\text{After-tax proceeds} = 23,000 - 2,160 = 20,840After-tax proceeds=23,000−2,160=20,840
Step 3: Calculate the growth of the proceeds over five years.You invest $20,840 at 2% interest, and the interest is taxed at 22% each year. We will calculate the after-tax interest and compound it annually.
Let’s denote:
  • Principal: P=20,840P = 20,840P=20,840
  • Interest rate: 2%
  • Tax on interest: 22%
  • Period: 5 years
Each year, the effective interest rate after tax is:
Effective interest rate=0.02×(1−0.22)=0.0156=1.56%\text{Effective interest rate} = 0.02 \times (1 - 0.22) = 0.0156 = 1.56\%Effective interest rate=0.02×(1−0.22)=0.0156=1.56%
Now, we calculate the value after 5 years using the compound interest formula:
A=P×(1+r)tA = P \times (1 + r)^tA=P×(1+r)t
Where:
  • P=20,840P = 20,840P=20,840
  • r=0.0156r = 0.0156r=0.0156 (after-tax interest rate)
  • t=5t = 5t=5 (years)
A=20,840×(1+0.0156)5A = 20,840 \times (1 + 0.0156)^5A=20,840×(1+0.0156)5
Let me calculate this:
After five years, the value of the investment in Scenario 1 (cashing the bond now and reinvesting) would be approximately $22,517.03.

Scenario 2: Hold the Bond to Maturity​

Step 1: Calculate the final value of the bond at maturity.The bond is currently worth $23,000 and pays 4% interest per year, compounded annually, over 5 years.
We will use the compound interest formula to calculate the value of the bond in 5 years:
A=P×(1+r)tA = P \times (1 + r)^tA=P×(1+r)t
Where:
  • P=23,000P = 23,000P=23,000
  • r=0.04r = 0.04r=0.04 (interest rate)
  • t=5t = 5t=5
Let me calculate this value:
After five years, the bond in Scenario 2 (holding it to maturity) would be worth approximately $27,983.02.
Step 2: Calculate the tax on the taxable interest ($18,000).You will pay tax at 24% on the $18,000 of taxable interest when the bond matures:
Tax=18,000×0.24=4,320\text{Tax} = 18,000 \times 0.24 = 4,320Tax=18,000×0.24=4,320
Step 3: Calculate the after-tax value at maturity.The final value of the bond after paying taxes is:
After-tax value=27,983.02−4,320=23,663.02\text{After-tax value} = 27,983.02 - 4,320 = 23,663.02After-tax value=27,983.02−4,320=23,663.02

Comparison of the Two Scenarios:​

  • Scenario 1 (cash now and invest): Final value = $22,517.03
  • Scenario 2 (hold to maturity): Final value = $23,663.02

Conclusion:​

Holding the bond to maturity (Scenario 2) yields a higher value of approximately $23,663.02, compared to cashing it now and reinvesting, which would result in $22,517.03. Therefore, it is better to hold the bond to maturity.
 
I watched all-in podcast this morning and they were talking about how impressive chat gpt o1 was at analyzing a cap sheet. That got me interested. I will probably buy a chat gpt subscription so I can play with it and see what it is like.
I am signed up for ChatGPT (free) and can access o1 preview. I think the free prompt limit is pretty small.
 
Assuming that the AI did not properly account for the annual tax loss in scenario 2, would adjusting the interest rate in the prompt compensate?

That is 0.02 x (1 - 0.24) = 0.0152 being the tax adjusted annual rate of return?
 
I can see what you mean about AI and math.

I changed the interest rate in the part of the prompt that affected scenario 2 and it made the mistake of thinking that the basis for scenario 1 was $23,000 instead of $5000 as it told it in the prompt.

Well at least it showed me the FV equation and helped me to think about it a little more clearly.

I guess I won't be hiring an AI accountant any time soon.
 
I agree with the conclusion, but not the AI's math on the second scenario.

Hold: Value in 5 years is $27.983 ($23,000*(1+4%)^5). At maturity, taxable interest is $22,983 ($27,983-$5,000) and tax is $5,516. After-tax proceeds are $22,467. Agree with AI.

Sell and reinvest: Maturty proceeds are $23,000 of which $18,000 is taxable interest and tax at 12% is $2,160, leaving $20,840 to reinvest. Agrees with AI so far. Future value is $22,517 ($20,840*(1+(2%*(1-22%)))^5).

AI failed to recognize that the 22% tax is paid each year rather than at the end of 5 years but the difference is insignificant and doesn't affect the conclusion.

ETA: My human response was more concise than the AI's response. Just sayin'.
 
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Thanks for taking the time to check it out. I had hoped to use AI to avoid bothering people, but I guess I will have to keep bothering.

Or perhaps learn how to do it myself . . .
 
I did not see this when posted. Unless something has changed on I-Bonds, you can, one time, change your method of reporting I-Bond interest. You can report all interest earned to date this year, pay taxes on that amount without cashing in your bonds, and then report interest earned every year going forward until you sell the bonds. I did this maybe 7 years ago on some 2001 I-Bonds I own. I report and pay taxes each year now. You could pay 12% now, and whatever amount your tax is each year going forward.
HTH, Dave
 
Thanks for the suggestion, but to change tax mode you have to pay all the accumulated tax and that is huge for me.
 
Thanks for the suggestion, but to change tax mode you have to pay all the accumulated tax and that is huge for me.
Per your numbers above, that is $2160. If using TD, you can partially sell, I think, to cover the taxes, if you wanted. I've never done that but "think" you can. HTH
 
Per your numbers above, that is $2160. If using TD, you can partially sell, I think, to cover the taxes, if you wanted. I've never done that but "think" you can. HTH
My example was for one bond but I have much more than that.
 
My example was for one bond but I have much more than that.
Well, it would have been nice to give complete info when asking for help. You can still sell as much as you need to pay the taxes on the ones you keep. You said they mature in 2030, so they were bought in 2000. Fixed rate in 2000 ranged from 3.4 to 3.6. So it would behoove you to keep as much as you can, depending on your tax rate jump. If you have a lot, you really need to do some planning. Good Luck.
 
I was asking for help checking the math. Not on what to do.

However, I appreciate you taking the time to discuss on the thread. Sorry if I was not clear.

Thanks.
 
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